Definition:
Named from the German 'quelle' (= source), common material of about 235 verses (Mark's gospel = 663) used by "Matthew" and "Luke" but not found in GMark.
Introduction:
This page is about demonstrating that the Q source, as (a) document(s), was put together after GMark was known and before GMatthew & GLuke were written. I start by showing "Q" dependance on GMark, then I'll proceed against the possibility the Q source was extracted from GMatthew (Farrer's hypothesis).

1) The evidence from the Mark-Q overlaps:

A) "Jesus and Beelzebub":
The best example of overlap is "Jesus and Beelzebub", Mt12:22-30 & Lk11:14-23, incorporating Mk3:23b-27 split in three sections (in navy blue).
Here is the "Q" version:
Mt12:22-30 "Then they brought him a demon-possessed man who was blind and mute, and Jesus healed him, so that he could both talk and see. All the people were astonished ...
But when the Pharisees heard this, they said, "It is only by Beelzebub, the prince of demons, that this fellow drives out demons."
Jesus knew their thoughts and said to them, "Every kingdom divided against itself will be ruined, and every city or household divided against itself will not stand. If Satan drives out Satan, he is divided against himself. How then can his kingdom stand? And if I drive out demons by Beelzebub, by whom do your people drive them out? So then, they will be your judges. But if I drive out demons by the Spirit of God, then the kingdom of God has come upon you. Or again, how can anyone enter a strong man's house and carry off his possessions unless he first ties up the strong man? Then he can rob his house. He who is not with me is against me, and he who does not gather with me scatters.""

It would be difficult to postulate this "Q" passage was written without Mark's gospel prior knowledge, or that "Mark" deleted part of some pre-existent "Q" material.
Rather, it seems a lot more plausible the "Q" author added up an exorcism as the cause of the ensuing alleged discussion, then some narrative to improve the readability, then a reassuring clarification that Jesus used "the Spirit of God" and not Beelzebub.
Also, since it is widely accepted that "Matthew" and "Luke" inserted their own material in Markan passages (as for Mt26:52-54, 27:19,24-25,51b-53,62-66, 28:2-4; Lk9:31b-32, 23:56), it should not be surprising the "Q" author(s) did the same.

More: in GMark and "Q", outside the "Jesus and Beelzebub" passage, the word 'Satan' (Greek 'satanas') occurs as such:
Mk = 3, "Q"(=GLuke) = 0
Note: "Matthew" most probably added "Away with you, Satan!" (4:10) in the "Q" temptation passage.

Therefore, it is most likely 'Satan' (and also 'Beelzebub' --see next note--) originated from GMark, and appears in "Q" because it "borrowed" Mk3:26.

Note: 2Kings1:8 describes Elijah in these words: "He was a man in a hairy [garment], and girt with a girdle of leather about his loins" (Darby), which is about the same as "Mark" depicted John the Baptist: "And John was clothed in camel's hair, and a leathern girdle about his loins," (1:6 Darby).
Because GMark suggests John is Elijah (9:11-13) (but rejected in Jn1:21), it is likely "Mark" knew about and used 2Ki1:8 to support his point. And it seems "Mark" got the god's name from the same passage because, in the whole O.T., 'Beelzebub' (or rather "Baal-Zebub, the god of Ekron" Darby) occurs only four times, all of them within the first sixteen verses of '2Kings' (1:3,4,6,16).

B) John and Jesus' baptisms:
On the following, could the "Q" author not know about GMark? Very unlikely
Mk1:7-8 "After me will come one more powerful than I, the thongs of whose sandals I am not worthy to stoop down and untie. I baptize you with water, but he will baptize you with the Holy Spirit."
"Q" Lk3:16 "... I baptize you with water. But one more powerful than I will come, the thongs of whose sandals I am not worthy to untie. He will baptize you with the Holy Spirit and with fire."
Let's notice the addition of "with fire" in the "Q" version. It fits very well with the "coloring" of the "Q" passage about "John's baptism". Because, within only three consecutive "Q" verses, it features the apocalyptic "fire" prominently, as shown in the next quote.
One question may be asked: why would a "Q" author use this part of GMark?
Because it links two "Q" passages, as follows (rewritten Markan material in navy blue):
Mt3:7-12 "You brood of vipers! Who warned you to flee from the coming wrath? Produce fruit in keeping with repentance. And do not think you can say to yourselves, 'We have Abraham as our father.' I tell you that out of these stones God can raise up children for Abraham. The ax is already at the root of the trees, and every tree that does not produce good fruit will be cut down and thrown into the fire.
I baptize you with water for repentance. But after me will come one who is more powerful than I, whose sandals I am not fit to carry. He will baptize you with the Holy Spirit and with fire.
His winnowing fork is in his hand, and he will clear his threshing floor, gathering his wheat into the barn and burning up the chaff with unquenchable fire."

C) The parable of the mustard seed:
The problematic "Q" and "Mark" overlaps can be explained the same way for the parable of the mustard seed: segments of GMark being rewritten with additional material put in.

a) Mark's version:
Mk4:30-32 "Again he said, "What shall we say the kingdom of God is like, or what parable shall we use to describe it? It is like a mustard seed, which is the smallest seed you plant in the ground.
[allusion to the smallness of the initial Christian message or/and origin]
` Yet when planted, it grows and becomes the largest of all garden plants,
[from a very little beginning, something unexpectantly large and strong can develop]
` with such big branches that the birds of the air can perch in its shade.""

The imagery is evidently borrowed from:
Eze17:23 "On the mountain height of Israel I will plant it; and it will bring forth boughs, and bear fruit, and be a majestic cedar. Under it will dwell birds of every sort; in the shadow of its branches they will dwell."

b) The "Q" version:
Lk13:18-19 "Then Jesus asked, "What is the kingdom of God like? What shall I compare it to [very similar with Mk4:30]? It is like a mustard seed, which a man took and planted in his garden. It grew and became a tree, and the birds of the air perched [also translated as "roosted"] in its branches""

A "Q" writer might have thought that a plant (black mustard), even if it grows up to almost four feet tall, is rather fragile and unlikely to be used as a perch or a roosting place for birds. Therefore, this author dispensed with the botanical details of "Mark" and replaced the frail plant by a more appropriate (solid, tall and long-lasting) tree (as in Eze17:23 quoted earlier). Furthermore a tree requires many years to grow (allowing for the tardy arrival of the Kingdom!), when the plant matures (and dies) in only one season.
In conclusion, the mustard seed parable in GMark presented serious flaws and was rewritten by a "Q" author.
He knew about Mark's version because the mustard seed was kept, even if there was no need to feature that particular seed. As a matter of fact, any (tree) seed would have been a lot more adequate.

PS: "Matthew" combined the two versions; consequently the plant is also a tree!
Mt13:32 "... the smallest of all your seeds, yet when it grows, it is the largest of garden plants and becomes a tree ..."

D) "Jesus' temptation":
Additional material (Lk4:2b-12, about 11 verses) about the alleged temptation in the desert appears to have been added. Why?
Likely because "Mark" had only a meager two verses about it, suspiciously too short:
Mk1:12-13 "At once
[isn't it apparent that "Mark" wanted to extract Jesus from John the Baptist's entourage?]
` the Spirit sent him out into the desert, and he was in the desert forty days, being tempted by Satan.
[but how, among sand and stones? No explanation is given by "Mark". "Q" will provide the answer]
` He was with the wild animals; and the angels attended him."

Now, let's look at the first part of the expanded "Q" version:
Lk4:1-3 "Then Jesus ... was led by the Spirit into the wilderness, being tempted for forty days by the devil. And in those days He ate nothing, and afterward, when they had ended, He was hungry. And the devil said to Him, "If You are the Son of God, command this stone to become bread."

Soon after, Jesus is "tested" again two more times (Lk4:5-13). Then why does "Q"(=GLuke) assert Jesus was tempted in the desert during the forty days, that is before the three temptations (narrated afterwards) occur later?
Likely to accommodate GMark, written earlier.

Notes:
a) In GMatthew 4:1 "Jesus was led ... to be tempted by the devil", but no temptations are told as happening within the forty days. But then, why bother mentioning (ahead of time) the devil's future testing, when the forty days are about fasting (Mt4:2), not temptations?
Overall, it appears "to be tempted by the devil" is due to GMark because in "Q"(=GMatthew) it is rather superflous & out-of-context.
But which is the version most faithful to "Q", Mt4:1-2 or Lk4:1-2?
I favor GLuke: why would "Luke" make a change introducing obvious incoherence? To be faithful to Mk1:13? But "Luke" was more prone than "Matthew" to delete & change GMark material.
b) Moses is not tempted in his forty days on mount Sinai (ex24-34). But he does not eat also!

E) From "sons of men" to "Son of man":
Mk3:28-29a Darby "Verily I say unto you, that all sins shall be forgiven to the sons of men, and all the injurious speeches [with] which they may speak injuriously; [29=>] but whosoever shall speak injuriously against the Holy Spirit, to eternity has no forgiveness; ..."

Mt12:31-32 Darby "For this reason I say unto you, Every sin and injurious speaking shall be forgiven to men, but speaking injuriously of the Spirit shall not be forgiven to men.
[32=>] And whosoever shall have spoken a word against the Son of man, it shall be forgiven him; but whosoever shall speak against the Holy Spirit, it shall not be forgiven him, ..."

Lk12:10 Darby "and whoever shall say a word against the Son of man it shall be forgiven him; but to him that speaks injuriously against the Holy Spirit it shall not be forgiven."

Let's notice how close is Mt12:32 relative to Lk12:10, almost word by word. The closest we have in GMark is Mk3:28-29a, which is "copied" (with some abbreviation) in Mt12:31 (but ignored in GLuke). And considering "Luke" located Lk12:10 at the end of a block containing a series of "Q" sayings (Lk12:2-9, corresponding to the one in Mt10:26b-33, in the same sequence), then it is rather certain Mt12:32 and Lk12:10 are "Q".
However, even if the overall meaning of Mk3:28 is different of the one in Mt12:32a/Lk12:10a, the wording of Mk3:28-29a is very similar to the one in Mt12:32 & Lk12:10 ("forgiven", "son(s)", "men/man", "injuriously", "speak(s) against the Holy Spirit" & "forgive...").
Consequently, "Q" Mt12:32/Lk12:10 appears to be rewritten from Mk3:28-29a, with "Son of man" in evidence as generally it is in "Q": Mk=14, "Q"=8 ("Q" being one third of GMark in size).
Also, the following statement, from "Q" itself, may have caused some of the content of "Q" Mt12:32/Lk12:10:
Lk7:34 Darby "The Son of man has come eating and drinking, and ye say, Behold an eater and wine-drinker, a friend of tax-gatherers and sinners;" (also in Mt11:19)

Notes:
a) Other isolated "Q" rewriting of GMark material: Mk4:22=>Mt10:26b/Lk12:2, Mk8:11-12=>Mt12:39/Lk11:29, Mk8:15=>Mt16:6/Lk12:1, Mk9:40=>Mt12:30a/Lk11:23a, etc.
b) Can we imagine "Matthew" created "Q" Mt12:32 and had the audacity to display his handywork right after his reproduction (with some compression) of Mk3:28-29a? I can't. Most likely, "Matthew" felt obligated to show two sayings coming from sources which had some credibility in his community: GMark & "Q".

2) "Q" main characteristics:

Besides the overlaps, the later dating of "Q" would explain many observations, among them:

A) "Q" is complementing and "correcting" Mark's gospel:

a) As explained in "HJ-1b", Section 9, "Mark" made a very weak & faulty argument about John preparing the way for Jesus as the Christ. In "Q" Lk7:26-27, Jesus himself describes the mission of John.

Note:
(Jesus saying:) "This is the one about whom it is written: "I will send my messenger ahead of you, who will prepare your way before you"" ("Q": Lk7:27b & Mt11:10b)
is very similar of
"I will send my messenger ahead of you, who will prepare your way." (Mk1:2b)
but shows notable differences with the only reference in the O.T., from 'Malachi':
"See, I will send my messenger, who will prepare the way before me [God]." (Mal3:1a)
suggesting this "Q" passage was lifted out from GMark, and not from the book of Malachi.

b) In GMark, nothing is written about John knowing about the person of Jesus. In "Q" Lk7:18-24, he does know!
Lk7:20 "When the men came to Jesus, they said, "John the Baptist sent us to you to ask, 'Are you the one who was to come, or should we expect someone else?'""

c) In Mk8:11b-12, an awkward statement raising doubts is made:
"To test him [Jesus], they ask him for a sign from heaven. He sighted deeply and said, "Why does this generation ask for a miraculous sign? I tell the truth, no sign will be given to it.""
In "Q", the problem seems to have been somewhat rectified:
Lk11:29,32b "Jesus said, "This is a wicked generation. It asks for a miraculous sign, but none will be given it except the sign of Jonah ...; for they [the Ninevites] repented at the preaching of Jonah, and now one greater than Jonah is here.""
The sign of Jonah is better than no sign at all!

PS: probably because this sign (Jesus outdoing Jonah about enticing people to repent) was not particularly convincing, "Matthew" will add to it:
Mt12:40 "For as Jonah was three days and three nights in the belly of a huge fish, so the Son of Man [Jesus] will be three days and three nights in the heart of the earth [Hades]
[but according to the gospel, Jesus' death lasts only forty hours!]."
Note: still later, there is an overabundance of signs:
Jn20:30-31a "Jesus did many other miraculous signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Christ, the Son of God, ..."
From no sign to one, then from only one to many!

d) "Mark" did not provide any explanation on why Jesus sends his disciples by themselves:
Mk6:6b-7 "Then Jesus went around teaching from village to village. Calling the Twelve to him, he sent them out two by two and gave them authority over evil spirits."
However, in "Q", the explanation is given:
Mt9:37-38 "Then he said to his disciples, "The harvest is plentiful but the workers are few. Ask the Lord of the harvest, therefore, to send out workers into his harvest field.""
The harvester (as Jesus) was featured in the Markan parable of the growing seed:
Mk4:26-29 "... As soon as the grain is ripe, he puts the sickle to it, because the harvest has come."

B) There are similarities and few contradictions between Mark's gospel and "Q":

a) In "Q", Jesus is the "Son of Man", from mortal to cosmic redeemer, (as in GMark):
Lk7:34 "'The Son of Man came eating and drinking, and you say, 'Here is a glutton and a drunkard, a friend of tax collectors and "sinners."'"
Lk9:58 "Jesus replied, "Foxes have holes and birds of the air have nests, but the Son of Man has no place to lay his head.""
who will come back unexpectedly:
Lk12:40 "You also must be ready, because the Son of Man will come at an hour when you do not expect him. [notice the similarities with Mk13:32-37!]"
Lk17:24 "For the Son of Man in his day will be like the lightning, which flashes and lights up the sky from one end to the other."
and during apocalyptic times:
Lk17:26-27 "Just as it was in the days of Noah, so also will it be in the days of the Son of Man. People were eating, drinking, marrying and being given in marriage up to the day Noah entered the ark. Then the flood came and destroyed them all."
Jesus, as the Son of Man, is more than a sage/teacher in "Q"! And the Son of Man's future coming would imply he left first!

b) In "Q", Jesus is also called "Lord" (Lk6:46,7:6,9:59,10:2) and "Son (of God/the Father)" (Lk4:3,9,10:22), as in the gospels.
However he is not called "Christ" or "Son of David". But in Mk8:29-30, only Peter calls him (once) "Christ", then "Jesus told them [the disciples] not to tell anyone about him". And in Mk12:35-37, "Mark" "demonstrated" that "the Lord" is not a descendant of David.
It seems "Q" followed GMark on both counts.

Now let's address the apparent disagreements between "Mark" and "Q":

c) The lack of material in "Q" about Jesus' Passion:
"Mark" considerably "elongated" it with controversial items, as I explained in "HJ-3a", Section 21 and "Parables and gospels", Section 5. Why add up more on an already long (and dubious) narrative! And then, "Q" is basically a collection of sayings, not of doings.
But there is a hint of the Passion in "Q", a cross being carried (Mt10:38, Lk14:27) by others than Jesus (as in Mk15:21). I'll come back to that later.

d) No resurrection appearance is mentioned in "Q", but GMark had none originally (see "HJ-3a", Section 21).

e) There is no mention of sacrifice (for the benefit of others) in "Q", but "Mark" suggested it in only two short passages:
Mk10:45b "... [Jesus] to give his life as a ransom for many."
Mk14:24 ""This is my blood of the covenant, which is poured out for many," he said to them."
Did "Q" think that was enough?
Was "Q" NOT warm to the concept of sacrifice?
Both questions can be answered by Yes, because Jesus is mainly perceived here as the "Son of Man" who will become the Savior, during a second coming. No sacrifice necessary!

3) Other argument for "Q" late dating:

a) When "Luke" and "Matthew" wrote their gospels, at about the same time, but for very different communities, they relied heavily on the one from "Mark". But they felt also obligated to insert the "Q" material. That suggests "Q" had a lot of credibility among the Christians of the time. But, if "Q" existed before GMark, why wasn't it included by "Mark"?

b) The following "Q" passage was evidently written after the destruction of Jerusalem:
Mt23:37-39 "O Jerusalem, Jerusalem, the one who kills the prophets and stones those who are sent to her!
[this passage appears to identify the "servants" in Mark's parable of the tenants:
Mk12:2-5 "... he [God] sent a servant to the tenants ... But they seized him, beat him ... Then he sent another servant to them; they struck this man on the head ... He sent still another, and that one they killed. He sent many others; some of them they beat, others they killed."]
` How often I wanted to gather your children together, as a hen gathers her chicks under her wings, but you were not willing! See! Your house is left to you desolate [as Jerusalem after 70]; for I say to you, you shall see Me no more till you say, 'Blessed is He who comes in the name of the LORD! [as in Mk11:9b!]'"
This is complemented by another "Q" passage:
Lk11:49-51 "Therefore the wisdom of God also said, 'I will send them prophets and apostles, and some of them they will kill and persecute,' that the blood of all the prophets which was shed from the foundation of the world may be required of this generation, from the blood of Abel to the blood of Zechariah who perished between the altar and the temple. Yes, I say to you, it shall be required of this generation
[reference to the massacre by the Romans of the people found in Jerusalem (70)!]."
Here, Jesus sounds like a prophet "I say to you, it shall ...", as he appears all along in GMark.

c) In Parables and gospels: Part 1, I took great pain in order to explain the genre of parable "à la Jesus" was created by the author of the earliest gospel, "Mark". That puts me in a small minority, but if the hypothesis is accepted, then the "Q" parables had to be generated later.
"Q" exhibits six parables, showing some of the same characteristics as the ones in GMark. See Parables and gospels: Part 2, Section 8, for comments on all the "Q" parables.

4) From Mark's gospel to "Q":

The progression from GMark to "Q" is also apparent in what follows:

a) Mk12:26-27a "Now about the dead rising -- have you not read in the book of Moses, in the account of the bush, how God said to him, `I am the God of Abraham, the God of Isaac, and the God of Jacob'? He is not the God of the dead, but of the living."
Here, as extrapolated from Exodus3:6a (because of the present tense in "am"), it is suggested (incidentally) that the three patriarchs are (or will be) alive (and consequently "proving" "dead rising", the main point).
But in "Q", that becomes a certitude:
Lk13:28 "There will be weeping there, and gnashing of teeth, when you see Abraham, Isaac and Jacob and all the prophets in the kingdom of God, but you yourselves thrown out."
The three patriarchs have become physical ("see") (and not just risen souls as in Philo's "The sacrifices of Abel and Cain, II"). And in Mk9:4, Moses and prophet Elijah have already been seen on the high mountain!

b) Lk7:22 "Go back and report to John what you have seen and heard: The blind receive sight, the lame walk, those who have leprosy are cured, the deaf hear, the dead are raised, ..."
This passage is obviously inspired from Isaiah29:18-19,35:5-6 (except for the dead). However, in the whole of "Q", there are no healing/revival stories about blind, lame, leper, deaf or dead. It seems the "Q" author (and his community) must have known of "references" in order to have Jesus claim that. Well, GMark has at least one specific narrated "example" for each:
- Blind cured: Mk8:25
- Lame (= paralytic and/or the "shriveled hand" man) cured: Mk2:12,3:5
- Leper cured: Mk1:42
- Deaf cured: Mk7:35
- Dead raised: Mk5:42
Remark: in GMatthew and GLuke, there is no account of deaf person(s) being cured.

c) In Mark's gospel, there are brief mentions of Jesus as the Son of God; but Jesus declares himself to be the Son only once (and NOT to his disciples or the crowds!):
Mk14:61b-62a "Again the high priest asked him, "Are you the Christ, the Son of the Blessed One?" "I am," said Jesus." Also in Mt26:63-64 & Lk22:70
But in "Q", the Christology is a lot more advanced:
Mt11:25-27 "At that time Jesus said, "I praise you, Father, Lord of heaven and earth, because you have hidden these things from the wise and learned, and revealed them to little children.
[little children only and not to adults? See next note]
` Yes, Father, for this was your good pleasure. All things have been committed to me by my Father. No one knows the Son except the Father, and no one knows the Father except the Son and those to whom the Son chooses to reveal him."
Note: "Q" does not provide any explanation about these "little children". However GMark does:
Mk10:15 "I tell you the truth, anyone who will not receive the kingdom of God like a little child [with innocence] will never enter it."

d) In GMark, Jesus is acknowledged as the "Son of God" by evil spirits (Mk1:24,3:11,5:7).
In "Q", the Devil himself knows about it (Lk4:3-11).

e) In Mk10:35-40, James and John ask Jesus some favors:
"Grant us that we may sit, one on Your right hand and the other on Your left, in Your glory [in heaven]."
Jesus objects to the specific request but suggests that prominent "seating" for the disciples is foreseen "but to sit on My right hand and on My left is not Mine to give, but it is for those for whom it is prepared."
In "Q", that becomes specified:
Mt19:28 "... when the Son of Man sits on the throne of His glory, you [the disciples] who have followed Me will also sit on twelve thrones, ..."

f) Mk4:22 "For whatever is hidden is meant to be disclosed, and whatever is concealed is meant to be brought out into the open."
In "Q", the statement becomes more direct and expanded upon as a militant "missionary directive":
Mt10:26-27: "... There is nothing concealed that will not be disclosed, or hidden that will not be made known. What I tell you in the dark, speak in the daylight; what is whispered in your ear, proclaim from the roofs."
GMark features a few "missionary directives" (Mk6:8-11) but "Q" added more (Lk10:3, 10:5-6, 10:9, 10:16a). In view of the emphasis in "Q" about these directives (and militancy), it is likely that Mk4:22 was reworked in order to become one of those.

g) Mk8:15 "... Watch out for the yeast of the Pharisees ..."
The "Q" version is more antagonistic:
Lk12:1 "Be on your guard against the yeast of the Pharisees ..."
In GMark, Mk8:15 is the one of the two worst things written against the Pharisees (without the teachers of the law), even if they are always represented testing Jesus.
But in "Q", they are four more woes against them and/or experts/teachers of the law (Lk11:42,46,47,52). That would explain the antagonistic twist!

Remark: the "woe" word (Greek 'ouai') seems to have started with Mark's gospel:
"woe": Mk = 2 (13:17 & 14:21), "Q" = 6, Mt = 14, Lk = 14
And also, it appears that "Mark" provided the prototype for the many "woe" diatribes against Pharisees and teachers/experts of the law in "Q" (4), GMatthew (7) and GLuke (6):
Mk12:38b-40a "Watch out for the teachers of the law. They like to walk around in flowing robes and be greeted in the marketplaces, and have the most important seats in the synagogues and the places of honor at banquets. They devour widows' houses and for a show make lengthy prayers."
echoed in:
Lk11:43 "Woe to you Pharisees,
[let's notice again the belligerent "Woe to ..." replacing the warning: "Watch out for ..."]
` because you love the most important seats in the synagogues and greetings in the marketplaces."

Notes:
a) The increased antagonism in "Q" seems also to have caused the change from:
Mk9:40 "for whoever is not against us is for us."
to "Q":
Lk11:23a "He who is not with me is against me ..."
b) In GMark, the teachers(/experts) of the law are worse enemies of Jesus than the Pharisees and they are mentioned more often:
"Pharisees"/"teachers (or experts) of the law": Mk = 12/20 as compared with Mt = 28/19 & Lk = 19/20

5) From "Q" to Matthew's gospel:

On the matter of hostility towards Pharisees and teachers of the law, a progression from "Q" to GMatthew is again rather evident:
There are only three (somewhat mild) diatribes against them in GMark (Mk7:6-13, 8:15, 12:38-40).
"Q" features five more:
Lk11:39-41 "... "Now then, you Pharisees clean the outside of the cup and dish, but inside you are full of greed and wickedness. You foolish people! Did not the one who made the outside make the inside also? ...""
Lk11:42, 11:46,
Lk11:47-48 "Woe to you [teachers of the law], because you build tombs for the prophets, and it was your forefathers who killed them. So you testify that you approve of what your forefathers did; they killed the prophets, and you build their tombs."
Lk11:52.
But there are as many as eleven of virulent diatribes in GMatthew, all of them towards the end: Mt23:3b, 23:5-7, 23:8-12, 23:13-14,
Mt23:15 "Woe to you, teachers of the law and Pharisees, you hypocrites! You travel over land and sea to win a single convert, and when he becomes one, you make him twice as much a son of hell as you are."
Mt23:16-22, 23:23-24, 23:25-26, 23:27-28, 23:29-32,
Mt23:33 "You snakes! You brood of vipers! How will you escape being condemned to hell?"

_{Here starts a segment about 'dating GMatthew'. The end will be indicated.}

Would it be a trend here with "Q" positioned between GMark and GMatthew?
Matthew's gospel was written when Pharisees (and teachers of the law) were turning into (righteous/virtuous) rabbis (teachers) and the Jewish religious leaders of the post-temple era:
Mt5:20a "For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven."
Mt23:2-3a "Then Jesus said to the crowds and to his disciples: "The teachers of the law and the Pharisees sit in Moses' seat. So you must obey them and do everything they tell you ...""
Mt23:6-7 "they love the place of honor at banquets and the most important seats in the synagogues; they love to be greeted in the marketplaces and to have men call them `Rabbi.' But you are not to be called `Rabbi,' for you have only one Master and you are all brothers."
All of this is corroborated in Josephus' Antiquities (published 93), XVIII, I, 3:
"... on account of which doctrines, they [the Pharisees] are able greatly to persuade the body of the people; and whatsoever they [the people] do about divine worship, prayers, and sacrifices, they perform them according to their direction [of the Pharisees/rabbis]; insomuch the cities gave great attestations to them on account to their entire virtuous conduct, both in the actions of their lives and their discourses also ..."

Notes:
a) In 'Wars', written some fifteen years earlier than 'Antiquities', the corresponding section in II, VIII, 14 does not describe the Pharisees as either teachers, or leaders, or having any appeal on other Jews.
b) As already mentioned, Pharisees are "second fiddle" to the teachers of the law in GMark but become predominant in GMatthew, written latter.
"Pharisees"/"teachers of the law": Mk = 12/20, Mt = 28/19

The Pharisees started to become rabbis after the time of distress (70-85?) following the destruction of Jerusalem. That gives us our best clue about the dating of Matthew's gospel (85-95?). And the "Q" passages about Pharisees and teachers of the law appear to have been written prior to that, when they were becoming more prominent (but not yet "rabbis") after the temple destruction. At that time (around 75-80), the "Q" author(s) saw these "proto-rabbis" as competition, started to unleash criticism on them and added up militant missionary directives. Later, when the emerging rabbis were seen as the enemies by some Jewish Christians (as "blind guides" Mt15:14), "Matthew" made up more virulent diatribes against them.
Mt23:13 "But woe to you, scribes and Pharisees, hypocrites! For you shut up the kingdom of heaven against men; for you neither go in yourselves, nor do you allow those who are entering to go in."

Notes:
a) "rabbis", as Pharisees becoming Jewish leaders, are only mentioned in GMatthew.
b) Jesus is called "rabbi" or "rabboni" in the gospels as follows:
Mk = 6, Mt = 2 (by only Judas the traitor), Lk = 0, Jn = 7

6) Arguments for separate "Q" document(s):

a) Let's consider:
Lk11:41a: "But give alms inwardly, and behold, all things are clean to you."
A scholar, Wellhausen, suggested that the Aramaic word dakkau (to cleanse, purify) was misread as zakkau (to give alms)
Then, if Lk11:41 was a mistranslation from the Aramaic, we would have near concordance with Mt23:26:
Mt23:26 "... First cleanse the inside of the cup, that the outside also may be clean"
Let's compare it with the "corrected":
Lk11:41a "But cleanse inwardly, and behold, all things are clean to you."
The "corrected" version would make more sense because, in Lk11:39b, what is inward is "greed and wickedness" and NOT goods for the poor:
Lk11:39-40a "... Now then, you Pharisees clean the outside of the cup and dish, but inside you are full of greed and wickedness. You foolish people! ..."
Let's compare it to the parallel "Q" passage in GMatthew:
Mt23:25 "... you hypocrites! You clean the outside of the cup and dish, but inside they are full of greed and self-indulgence."

b) Let's also consider:
Lk14:26 "If anyone comes to me and does not hate his father and mother ... brothers and sisters ..., he cannot be my disciple."
First, let's examine the parallel saying from "Matthew":
Mt10:37 "He who loves father or mother more than Me is not worthy of Me. And he who loves son or daughter more than Me is not worthy of Me."
In the later gospel, "hates" is replaced by "loves", the negation removed and a "more" clause added. As a result, the saying makes some sense, and very much in tune with:
Mk3:32-35 "...they said to Him, "Look, Your mother and Your brothers are outside seeking You." But He answered them, saying, "Who is My mother, or My brothers?" And He looked around in a circle at those who sat about Him, and said, "Here are My mother and My brothers! For whoever does the will of God is My brother and My sister and mother.""
Jesus prefers believers to his own blood family and expects the same from others:
Mk10:29-30 "... Assuredly, I say to you, there is no one who has left ... brothers or sisters or father or mother or wife or children ..., for My sake and the gospel's, who shall not receive ... brothers and sisters and mothers and children ..."
Here, as a (harsh) development, the Christian is promised a new extended family of believers if he is separated from his own blood family.
But there is no notion of hate against the blood relatives!
Even Mt10:35 and the parallel Lk12:51-53, written because the new faith was breaking families apart (some joined, the others did not, creating internal conflicts), do not say anything about "hate", just state the facts known by early Christians.
But "If anyone comes to me and does not hate his father and mother ... brothers and sisters ..., he cannot be my disciple." (Lk14:26)
is probably the ugliest statements put in the mouth of Jesus in all the gospels.

Then, according to Aramaic scholar Jack Kilmon:
"The interesting interface between Aramaic and Greek is that where Greek has many words for one meaning, Aramaic ... a "meat and potatoes" language ... has one word with several meanings ..."
"The Aramaic of Luke's source document, in part, was: "man daTHE l'WAti w'LA SAne l'ABuhy w'l'IMMeh....." whoever comes to me and does not "hate" his father and mother ...
The word "hate" in Aramaic, however, is an idiom meaning "to set aside." The saying was originally to SET ASIDE your mother, father, brothers, sisters, to follow Jesus ..."
If "corrected", then we would have:
Lk14:26 "If anyone comes to me and does not set aside his father and mother ..., his brothers and sisters, ... he cannot be my disciple."
This "corrected" version would be very close of:
Mt10:37a "Anyone who loves his father or mother more than me is not worthy of me ..."
Now, let's go back to:
Lk14:26 "If anyone comes to me and does not hate his father and mother, his wife and children, his brothers and sisters-- yes, even his own life --he cannot be my disciple."
It seems that "Luke" added "yes, even his own life" to attenuate the awful idea of hate towards the family members. Obviously, the "Q" passage was deemed embarrassing. Consequently, in order to soften the blow, the "hate" was redistributed to everyone in the family, including the would-be disciple. That does alleviate the notion of hate from him to his relatives.
From Jack Kilmon again: "... a "Q" saying evolved from an Aramaic source document and therefore was a source for Luke, Matthew and Thomas."

Note: "Luke" could have replaced "does not hate" by something like "does not set aside" or "prefers", but did not. Instead the author added up "yes, even his own life". That shows that "Luke" was reluctant to change the wording of a "Q" saying. Consequently, the "correction" was made by a small insertion.

With the "corrections", Lk11:41a & Lk14:26 are very close to passages appearing only in GMatthew (Mt23:26 & Mt10:37) and consequently would be "Q" sayings. And the errors are easily explained from the translation of Aramaic to Greek. So, it is very likely that part of the "Q" document(s) was written in Aramaic from (authentic and unauthentic) material.

Note: let's compare Mt6:12 "Forgive us our debts ..." with Lk11:4 "Forgive us our sins ..."
"debts" & "sins" appear to be a translation of the Aramaic word 'xwbyn', which means 'debts' but also 'sins'. It seems the "Lord's prayer" was first composed in Aramaic but got translated differently.

I demonstrated already that:
a) "Q" was compiled from independent sources, sometimes erroneously translated (as shown in preceding Section).
b) "Q" predated GMatthew (as shown in Section 5).

But more arguments can be made to prove that "Q" was not extracted from GMatthew. Here is one of them. But first, I want to give my special thanks to Mark Goodacre, an ardent proponent of the Farrer's hypothesis, who, through a friendly debate, enticed me to put together what follows:

Let's start by noticing the anxiety about food, as spelled out in the "Lord's prayer":
"Q" Mt6:11 "Give us this day our daily bread."
The same notion is amplified in:
"Q" Lk6:20 "Blessed are you who hunger now, for you will be satisfied"
"who hunger now" are evidently the poor to whom getting daily food is a big worry and not always obtainable. However in the corresponding verse of:
"Q" Mt5:6 "Blessed are those who hunger and thirst for righteousness, for they will be filled."
the addition makes the hungry ones NOT the poor people but those striving "for righteousness".

Again the same notion of anxiety about food is expressed in:
"Q" Lk12:29-31 "And do not set your heart on what you will eat or drink; do not worry about it. For the pagan world runs after all such things, and your Father knows that you need them. But seek his kingdom, and these things [food and drink] will be given to you as well."
Now let's observe the corresponding passage in:
"Q" Mt6:31-33 "So do not worry, saying, `What shall we eat?' or `What shall we drink?' or `What shall we wear?'
[only poor would have these worries. Also let's notice the addition about wearing (clothes): why would "Luke" delete that, more so considering Lk12:27-28?]
` For the pagans run after all these things, and your heavenly Father knows that you need them. But seek first his kingdom and his righteousness, and all these things will be given to you as well."
Here again the word 'righteousness' appears to be added.

But then "Matthew" made a lot of use of 'righteous' or 'righteousness' in his gospel. According to the NIV:
"Q"(=GLuke): 'righteous' = 0, 'righteousness' = 0
GMark: 'righteous' = 2, 'righteousness' = 0
GMatthew: 'righteous' = 15, 'righteousness' = 6
GJohn: 'righteous' = 1, 'righteousness' = 2

In all of "Q", 'righteousness' is only in the two Q(=GMatthew) passages as quoted previously: Mt6:31-33 and Mt5:6. Except for these two likely insertions, "Q" is without 'righteousness'. This word does not appear in GMark and in "Q"(=GLuke), even if "Luke" was not opposed to use 'righteous' or 'righteousness':
GLuke: 'righteous' = 6, 'righteousness' = 2
So the apparent inclusion of 'righteousness' in the two "Q" passages of GMatthew is likely due to the author's coloring.

There is more:
"Q" Lk6:20b "Blessed are you who are poor, for yours is the kingdom of God."
But in the corresponding passage in GMatthew, we have:
"Q" Mt5:3 "Blessed are the poor in spirit, for theirs is the kingdom of heaven [God]."
"poor in spirit" does not appear anywhere else in the whole Bible. Obviously, this expression was also prone to attract derogatory remarks. Then why would "Matthew" use it?
Again, to prevent the (materially) poor as appearing to be the beneficiaries of the Kingdom.

Notes:
a) Mt5:5, seemingly a Matthean parallel saying of Mt5:3, suggests who these "poor in spirit" may be:
"Blessed are the meek, For they shall inherit the earth."
This is drawn from Psalm37 "... But the meek shall inherit the earth, ..." (11); and also appearing in the same psalm: "... The righteous [Jews] shall inherit the land, ..." (29).
And we also have, and only in GMatthew:
Mt5:10 "Blessed are those who are persecuted for righteousness' sake, for theirs is the kingdom of heaven."
So now the ones inheriting the Kingdom are the meek/righteous, not the poor. This is confirmed by the following verses:
Mt5:20 "For I say to you, that unless your righteousness exceeds the righteousness of the scribes and Pharisees, you will by no means enter the kingdom of heaven."
Mt25:46 "[after the Judgment] Then they will go away to eternal punishment, but the righteous [wealthy enough to be generous for the destitutes (25:34-44)] to eternal life."
b) "poor of spirit" shows in the DSS war scroll and may mean here "disheartened" or even "coward":
"... to raise up in judgment those whose heart has melted, to open a mouth for the dumb to sing God's mighty deeds, and to teach feeble hands warfare. He gives those whose knees shake strength to stand, and strengthens those who have been smitten from the hips to the shoulder. Among the poor in spirit [ . . . ] a hard heart, ..."

This is confirmed by Matthew's handling of a particular passage from GMark, alluding to the chosen ones for the Kingdom:
Mt19:16b-21 ""... What good thing [no plural] must I [a rich man] do to get eternal life [by entering the Kingdom (19:23-24)]?" ... Jesus replied ... obey the commandments ...
[here, obeying the commandments is the only "good thing" required to be an elect]
` "what do I [the rich man] still lack?" Jesus answered "if you want to be perfect, go, sell your possessions and give to the poor,
[to enter the Kingdom => obey the commandments; to be perfect => in addition, sell what you own] ...""

But in GMark, which "Matthew" had:
Mk10:17b-21 ""What must I [the rich man] do to inherit eternal life?"... he declared, "all these [commandments] I have kept since I am a boy ... "one thing you lack," he [Jesus] said. "Go, sell everything you have [consequently become poor yourself!] and give to the poor ...""

PS: Luke's version:
Lk18:22 "... Sell everything you have and give to the poor, ..."

From Mk10:17-21 and Lk18:18-22, "sell everything you have" is absolutely needed in order to be an elect.
In Mt19:16-21, "sell ["all" not specified] your possessions" is required "to be perfect"; but for entering the Kingdom, it is NOT mandatory (obeying the commandments is good enough).

Needless to say, other early pieces of evidence, including those in GMark and James' letter (which "Matthew" likely had when writing his gospel), support the interest of Jesus (and latter "direct" followers) for the poor:
a) Jesus was poor by birth, by being one of (at least) seven children of a rural family (Mk6:3, Mt13:55-56a).
b) Jesus' poverty is corroborated by Paul in:
2Co8:9b " yet for your sakes he [incarnated Jesus] became poor, so that you through his poverty might become rich."
c) Mk10:23-25 "Jesus looked around and said to his disciples, "How hard it is for the rich to enter the kingdom of God!" ... "It is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God.""
d) James2:5 "Listen, my dear brothers: Has not God chosen those who are poor in the eyes of the world to be rich in faith and to inherit the kingdom he promised those who love him?"

Conclusion: in the case of the "Q" sayings about the elects of the Kingdom, it was "Matthew" who modified them (by blatantly inserting his own words) to satisfy his agenda: replace the poor by the meek/righteous.

Notes:
a) Another Matthean insertion (in bold) within "Q" material, also fully explained by Matthew's agenda (that is obeying the whole Mosaic Law):
Mt4:4 "But He answered and said, "It is written, "Man shall not live by bread alone, but by every word that proceeds from the mouth of God [the Law (see Mt5:18-19,22:2-3 below), as the righteous should live by]."'"
Let's compare it with:
Mt7:21 "Not everyone who says to Me, "Lord, Lord,' shall enter the kingdom of heaven, but he who does the will of My Father in heaven [follows God's words]."'"
Here are Mt5:18-19 & 22:2-3 ("Q" material in italics), confirming "Matthew" full acceptance of the law of Moses (dictated by God!):
Mt5:18-19 NASB "For truly I say to you, until heaven and earth pass away, not the smallest letter or stroke shall pass from the Law until all is accomplished.
Whoever then annuls one of the least of these commandments, and teaches others to do the same, shall be called least in the kingdom of heaven; but whoever keeps and teaches them, he shall be called great in the kingdom of heaven."
Mt22:2-3 "... The scribes and the Pharisees sit in Moses' seat. Therefore whatever they tell you to observe, that observe and do ..."
b) Another Matthean insertion (in bold) within "Q" material, also fully explained by Matthew's agenda (Jesus as the Son of David):
Mt12:23 "And all the multitudes were amazed and said, "Could this be the Son of David?""
("Son of David": Mk = 3, (Q = 0), Mt = 10, Lk = 4, Jn = 0)
"Matthew" inserted also "Son of David" within Markan material, as in Mt15:22 & Mt21:9.

"Nero [54-68C.E.] slightly debases the gold and silver coinages, a practice copied by some later emperors, starting mild but prolonged inflation.
p 95" (A History of Money from Ancient Times to the Present Day by Glyn Davies, rev. ed. Cardiff: University of Wales Press, 1996)

But the most compelling argument against the Farrer's hypothesis (or the three sources one, 3SH) would be:
If "Luke" had GMatthew, why (with the exception of "Q" and common GMark material) are so many differences and conflicts between the two gospels? The "problem" is generally ignored or, at best, scantily addressed.
And why "Luke" did not implement Matthean material most agreeable, such as:
- Mt20:1-16, never too late to join (or rejoin) the Christian brotherhood (see Lk15:11-32)
- Mt25:35-45, charity to the destitute and poor, in order to enter the Kingdom (see Lk6:34-35,10:30-37,11:5-8,14:13-14,16:9,19-28,19:8-9)
- Mt27:19, a Roman woman declaring Jesus as a "righteous/just" ('dikaios') man (see Lk23:47, a centurion saying the same). This could not have been missed by "Luke", considering the pro-feminist and pro-Roman stance of the gospel & 'Acts' (as explained here).
More so when "Luke" reproduced a "Q" saying dead against the author's Gentile outlook (Lk2:29-32,7:4-10, Ac10:1-48,11:1-18, etc.):
Lk16:17 "It is easier for heaven and earth to disappear than for the least stroke of a pen to drop out of the Law." (parallel Mt5:18)

Note: "least stroke of a pen. The Greek word for this phrase means "horn" and was used to designate the slight embellishment or extension of certain letters of the Hebrew alphabet." (NIV Study Bible, note on Mt5:18)

And also, going back to the Farrer's hypothesis, how can we explain Luke's rewriting in what follows?
From:
"He who loves father or mother more than Me is not worthy of Me. ..." (Mt10:37)
to
"If anyone comes to me and does not hate his father and mother ..., he cannot be my disciple." (Lk14:26)
considering "Luke" reproduced "honor your father and mother" from GMark (Lk18:20/Mk10:19) and "love your enemies" from "Q" (Lk6:27,35/Mt5:44).
As I said, "Luke" accepted "Q" sayings, even when they hurt.

Three specific minor agreements between GMatthew and GLuke against GMark are often mentioned as a reason "Luke" knew about Matthew's gospel. They are the parable of the mustard seed (already addressed), "Nazara" (Mt4:13, Lk4:16) and "Who is the one who struck You?" (Mt26:68, Lk22:64).

a) "Nazara":
Mt4:12b-13a "... He departed to Galilee. And leaving Nazara, He came and dwelt in Capernaum, ..."
Lk4:14-16a "Then Jesus returned ... to Galilee, ... Nazara, where He had been brought up ... ["He went down to Capernaum" (Lk4:31)]"

- First, let's notice the two quoted passages have similarities. However in GMark1:14 "Jesus came to Galilee, ...", there is no mention of Nazareth/Nazara. That would indicate these passages may be "Q" material.
- Secondly, both authors reasserted that Nazareth (Nazara) is the hometown of Jesus after they had mentioned it already (Mt2:22-23, Lk1:26,2:39). This redundancy can be explained by both authors complying with "Q", without consideration about what they wrote before.
- Thirdly, Mt4:12-13a/Lk4:14-16a follows immediately the "Q" 'temptation of Jesus' (Mt4:1-11, Lk4:1-13). Consequently this passage was probably the ending of the 'temptation' sequence and therefore part of "Q". Also the "Nazara" section, as a small "Q" "geographical" narrative attached to a longer "Q" story (the temptation), has a counterpart, 'the centurion' (Mt8:5:13, Lk7:1-10), which begins with "... when Jesus had entered Capernaum ..." (Mt8:5a, Lk7:1b).

"Luke" added on a lot of material in 4:14-31, including an early visit to Nazareth (4:16-30). But because this visit is:
a) not related in any other gospels.
b) "loaded" with theological connotations very much according to the author's inclination.
c) featuring Jesus as known for his miracles in Capernaum (4:23) before they happen there (4:35,39-40)
it is apparent "Luke" considerably altered the "Q" passage (4:14-16) to fit the author's agenda.

But why 'Nazara', instead of 'Nazareth'?
a) A "Q" author might have felt the need to reassert Nazara/Nazareth as the hometown of Jesus: in GMark, 'Nazareth' appears only once "... Jesus came from Nazareth of Galilee ..." (1:9) and when Jesus goes to the village where his mother, brothers and relatives live, 'Nazareth' is not mentioned, just "his hometown" (6:1-6).
b) This author may have intended to provide a more correct translation for Jesus' village. Nazareth, a small locality then in the Aramaic speaking Galilee, most likely did not have an "official" Greek name. Therefore "translations" could be different. As an example, Josephus provided two Greek appellations for "Capernaum" (Greek: 'kapernaum'): 'kafarnaoum' (Wars,III,X,8) and 'kefarnwkon' (Life72)

b) "Who is the one who struck You?" (Mt26:68, Lk22:64):
Mk14:65 "Then some began to spit on Him, and to blindfold Him, and to beat Him, and to say to Him, "Prophesy!" And the officers struck Him with the palms of their hands."
Mt26:67-68 "Then they spat in His face and beat Him; and others struck Him with the palms of their hands, saying, "Prophesy to us, Christ! Who is the one who struck You?""
Lk22:63-64 "Now the men who held Jesus mocked Him and beat Him. And having blindfolded Him, they struck Him on the face and asked Him, saying, "Prophesy! Who is the one who struck You?""

Could "Who ... struck you?" be a small "Q" item?
Very likely NOT:
- "Q" has no other Passion narrative/saying.
- It is not a Jesus' saying (or John's).
- The rest of the narrative is drawn from GMark, with minor alterations.
GMark has Jesus being asked to prophecy while being beaten. That's rather unrealistic and it is highly probable one of the later synoptic authors added on "Who ... struck you?". But which one?
Considering the addition does not make much sense if Jesus can see, the answer has to be "Luke": in GLuke, as in GMark, Jesus is blindfolded; in GMatthew, there is no mention of it. Now let's ask ourselves why would "Matthew" remove 'Jesus blindfolded' if he wrote next "who is the one who struck you?"? The answer can only be "Matthew" had no use of 'Jesus blindfolded' because he did not write anything about the guards' question.
Then, what would happen next?
An early copyist added up "Who ... struck you?" when making copies of GMatthew, according to what he read in GLuke. This is why "Who ... struck you?" appears with the same five consecutive Greek words in both gospels, which is at odd with the rest of the (dissimilar) wording in Mt26:67-68 & Lk22:63-64.
Later, eager to issue "complete" copies of the gospel, other copyists followed suit, causing all the most ancient manuscripts at our disposal (late 3rd to 4th century) to show the addition.

Note: later alterations (easily detectable when showing as discrepancies between the oldest copies) are common in gospels and epistles. Concerning GMatthew, according to the NIV Study Bible, ancient copies do not agree on the following verses, which show addition (<=> lack) or rewording:
5:22,44, 6:13, 8:28, 12:47, 15:6,14, 16:2,3, 17:20,21, 18:10,11,15, 19:29, 21:44, 23:13,14, 24:36, 26:28 & 27:35,46
Let's consider:
Mt21:44 "He who falls on this stone will be broken to pieces, but he on whom it falls will be crushed."
and
Lk20:18 "Everyone who falls on that stone will be broken to pieces, but he on whom it falls will be crushed."
Let's notice how similar is the wording. Because this saying has no counterpart in GMark, it would be considered "Q" material. So what's the point?
Mt21:44 does not appear in some ancient manuscripts (but most modern Bibles do carry it) and is likely a later "harmonization" from GLuke (as it is suspected for Mt26:68b "Who is the one who struck You?").
But could an addition be done on all ancient copies of GMatthew?
In "Parables and gospels, Sections 8 to 10", I showed the two Jesus' reappearances were added on by different authors (none of them "Matthew").

8) Cynicism and sandals:

The "missionary directives" (Mk6:8-11, Mt10:9-14, Lk9:3-5,10:2-12) are considered also one of the Mark-Q overlaps. In the Markan segment, we have:
Mk6:8-9 "These were his instructions: "Take nothing for the journey except a staff --no bread, no bag, no money in your belts. Wear sandals but not an extra tunic.""

Note: let's notice "Mark" certainly never thought of Jesus as barefooted:
Mk1:7b "... whose sandals I [John the Baptist] am not worthy to stoop down and untie."

Note: other extreme (& socially unworkable!) cynic-like sayings appearing in "Q":
Lk6:29 "To him who strikes you on the one cheek, offer the other also. And from him who takes away your cloak, do not withhold your tunic either."
(which Jesus is never said to have done in the gospels!)

9) Last remarks:

Up to the 1970's, a near consensus existed among critical scholars, stating "Q" was compiled around 80.

According to my insight, it was done by (Gentiles tolerant) Jewish Christian(s) (Lk16:17,22:30) in Antioch, Syria.

Note: why Antioch?
Because it is the likely origin of GMatthew which is remarkably "in tune" with "Q" in the area of terminology and themes, as already shown in "Parables and gospels", Section 9.
But why would GMark (known by the "Q" people), despite its flaws and Gentile outlook, be well received into a Jewish Christian community?
Because it explained (and "prophesied") the destruction of Jerusalem and its people: God avenging his Son (Mk12:1-9), taking precedence over the King not coming back to defend the holy city (the least that could be expected from a Messiah!). Explanations are in "Parables and gospels", Section 5.

So, what happened?
In the 1970's, most studies on the "historical Jesus" were based on the gospels, especially Mark's one. Many conflicts and historical impossibilities surfaced, more so in regard of Jesus' Passion (with the trials).
Then mainly because of "Q" Mt10:10/Lk10:4 (as for the itinerant Cynics, the disciples allegedly NOT wearing sandals), it was extrapolated Jesus had to be a pseudo-Cynic sage, even if Cynicism was dormant for most of the first century.
And since "Q" does not have the objectionable Passion story and is considered (wrongly) "primitive", "Q" (or part of it) was deemed more trustworthy and therefore written earlier than the (unreliable) gospels, when embellishments & outright fiction would be incorporated into them. "Q" was in, "Mark" was out: the trend is set.
Counter arguments:
a) "Q" is mostly a collection of sayings and parables, with little narrative material. Consequently, any Passion narrative would look out of place in "Q".
b) Modern scholars (and myself) flagged out many items in Jesus' final days in Jerusalem as being historically implausible. Early Christians, closer in time to the alleged events, would have felt the same way: many elements in Mark's elongated Passion are fictional (and added on for an obvious purpose, as explained in "HJ-3a", Section 21 and "Parables and gospels", Section 5). Consequently, there was no incentive or need to add any material on a contentious & already long Passion narrative.
Furthermore, the word "cross" (being carried as in Mk15:21) appears in "Q":
Mt10:38 "and anyone who does not take his cross and follow me is not worthy of me." (Lk14:27)
suggesting that Jesus' crucifixion (a part of the Passion) was known by the "Q" author(s).
c) Mark's gospel is deemed "written later" because of its contentious items. But "Q" introduces also its own ones. As example, and drawn from Jesus' alleged (and unwitnessed) temptation in the desert:
Lk4:1-2 "... Jesus, ... tempted for forty days by the devil. And in those days He ate nothing, and afterward, when they had ended, He was hungry [quite an understatement!]."
Lk4:5 "Then the devil, taking Him up on a high mountain, showed Him all the kingdoms of the world in a moment of time
[no high mountain allows anyone to see all the earth!]."

However many scholars, for various motives, followed suit and collected an array of (mostly) sayings, those they eagerly (and with no evidence whatsoever) dated as pre-gospels, including the uncanonical gospel of Thomas (GThomas), or part of it, which has its own believers.

Notes:
a) If parts of those writings appear to be "dated" (late), they are tagged as subsequent added "layer(s)". Then the dateless expurgated version is claimed "early" by some leap of faith.
b) An early (but unproven) existence of a 'Gospel of signs' & a Passion story is also postulated by some, in order to explain GJohn is not dependant on earlier gospels. But as I demonstrated in these pages, "John" knew about some of the Synoptics when composing his gospel.
c) Scholars who are separating "Q" in different strata (acknowledging parts of "Q" as late) do not agree with each other (and have many critics!), coming up with different "solutions". One of those, John Kloppenborg, probably the best known in this field, considerably changed his "model" and acknowledged candidly: "I might say at this point that I regard my stratigraphic proposals in Formation [of Q] and ExQ ['Excavating Q'] as interesting bits of guesswork, like Pentateuchal criticism. If it actually helps clarify the final state of the text, fine. If it doesn't, drop it. If another model comes along to make better sense of the text, then drop or modify my model. We are playing a heuristic game here, not trying to recreate the composition process; that, epistemologically, is completely beyond our capabilities." (Synoptic-S, On-line Seminar, Oct. 2000)

Now here is the second argument for the early dating of "Q":
Collections of sayings appear first, then the pseudo-biography of the "sayer" is written next.
Counter arguments:
a) To my knowledge, the main example provided to "prove" the aforementioned "dogma" is "Q" & GThomas (a collection of saying & parables) preceding GMark. That would be a circular argument!
b) GThomas is contested by many scholars (and myself) as being "early", and for many reasons. Even the Jesus Seminar does not have (anymore) GThomas as written before the gospels (70-100), but rather, at times, dependant on those. See The gospel of Thomas

Other proposals exist, such as:
a) "Q" being a stand-alone mini-gospel pre-dating GMark
b) The aforementioned Farrer's hypothesis, that is with "Q" somehow being spirited out from GMatthew to GLuke: James Hardy Ropes (1934), Austin Marsden Farrer (1955) & Michael Douglas Goulder (1974, 1989)
c) The opposite view, with "Q" coming from GLuke to GMatthew: Christian Gottlieb Wilke (1838), Bruno Bauer (1841), Ronald V. Huggins (1992) & Evan Powell (2006)

But the one I laid out on that page is the simplest, the most substantiated and with the least "problems".

A good entry point for the debate, learned opinions and info about "Q" is:
http://www.earlychristianwritings.com/q.html
I recommend Peter Kirby's article, The Existence of Q