Counterexample

A counterexample is a specific case which shows that a general statement is false.

Example 1:

Provide a counterexample to show that the statement

"Every quadrilateral has at least two congruent sides"

is not always true.

Any scalene quadrilateral will serve as a counterexample.

For a conditional (if-then) statement, a counterexample must be an instance which satisfies the hypothesis, but not the conclusion.

Example 2:

Provide a counterexample to show that the statement

If , then

is not true for all real numbers p, q, and x.

Let p = 1, q = 0 and x = 0.

Then but , since division by 0 is undefined.