CONJECTURE

is a conclusion based on examples.

COUNTEREXAMPLE

is an example that shows a conjecture is to be false.

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.

0

If 1 is added to an off number, the result is always an even number

1 squared=1

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.