CONJECTURE is a conclusion based on examples.
COUNTEREXAMPLE is an example that shows a conjecture is to be false.
Example of Conjectures for a rectangle
a) If a quadrilateral has four equal angles, it has four equal sides.
b) The length of a rectangle is always double its width
c) The opposite sides of a parallelogram are equal in length.
Out of the three conjectures given, a) and b) are the counterexamples.
Examples of false conjecture with their true counterexamples
A number that is not positive is negative.
If 1 is added to an off number, the result is always an even number
The altitude of a triangle always lies inside the triangle
An altitude of an obtuse triangle lies outside it.
Every rectangle is a square
Any rectangle in which its length is not equal to its width is not a square.