Final answer:
The statement "for every integer p, if p is prime then p^2 − 1 is even" is disproven by the counterexample p = 3.
Step-by-step explanation:
The statement "for every integer p, if p is prime then p2 − 1 is even" can be disproven by providing a counterexample. Let's consider the prime number p = 3. If we substitute p = 3 into the statement, we get 32 - 1 = 8, which is not even. Therefore, the statement is false. Thus, the counterexample is p = 3.