CS-07 DISCRETE
MATHEMATICS JUNE 1998
| Time: 3 Hours |
Max. Marks: 75 |
Note: Question no. 1 is compulsory. Answer any three from the rest
| 1. | . | In about one short paragraph, explain the meaning of the following words or phrase : |
| (i) Tautology | ||
| (ii) Automatic proving of theorems | ||
| (iii) Predicates | ||
| (iv) Adjacency matrix of a graph | ||
| (v) Partition of a set | ||
| (vi) i-v fuzzy set | ||
| 2. | (a). | Prove that if R be an equivalence relation in a set A, then R-1 is also an equivalence relation in A. |
| (b). | If A = {14, 15}, B = {16, 17} and C = {17, 18} find {A x B} U {B x C}. | |
| 3. | What are chains ? Outline the proof of the theorem that every chain is a distributive lattice. | |
| 4. | (a). | What is a bipartite graph ? What is a complete bipartite graph ? Illustrate with an example of each. |
| (b). | State Cayley's theorem regarding spanning trees. How many spanning trees will be there for the following graph : | |
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| 5. | Define and explain with examples the concept of a finite state machine. What are transition diagrams ? Draw the transition diagram of a serial binary adder. | |
| 6. | (a). | Define and illustrate with examples, the
meaning of membership function in a fuzzy set. Draw a diagram to
illustrate what the membership function of a 'crisp' set would look like ? |
| (b). | If x = {51, 52, 53, 54}
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| then what is the value of A U B ? |