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 , , and .
Let , and .
Then but , since division by is undefined.