The statement "if a number is a perfect square then the number is an even number" is false because not all perfect squares are even. A counterexample to this statement is the perfect square of the number 1.
- The perfect square of 1 is \(1^2 = 1\).
- The number 1 is an odd number.
Thus, this shows that it is possible for a perfect square to be an odd number, providing a counterexample to the original statement.
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