Disprove the following statement by giving a counterexample. For every integer p, if p is prime then p2 - 1 is even. Counterexample: Consider the ordered pair (p, p² – 1) = The values in the ordered pair show that the given statement is false because (choose one) p is prime and p² – 1 is even. p is prime and p? - 1 is not even. O p is not prime and p2 – 1 is even. p is not prime and p2 - 1 is not even. Need Help? Read It Watch It
Disprove the following statement by giving a counterexample. For every integer p, if p is prime then p2 - 1 is even. Counterexample: Consider the ordered pair (p, p² – 1) = The values in the ordered pair show that the given statement is false because (choose one) p is prime and p² – 1 is even. p is prime and p? - 1 is not even. O p is not prime and p2 – 1 is even. p is not prime and p2 - 1 is not even. Need Help? Read It Watch It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Disprove the following statement by giving a counterexample.**
For every integer \( p \), if \( p \) is prime then \( p^2 - 1 \) is even.
**Counterexample:** Consider the ordered pair \( (p, p^2 - 1) = \left(\text{______}\right) \).
The values in the ordered pair show that the given statement is false because (choose one):
- \( p \) is prime and \( p^2 - 1 \) is even.
- **\( p \) is prime and \( p^2 - 1 \) is not even.** (selected)
- \( p \) is not prime and \( p^2 - 1 \) is even.
- \( p \) is not prime and \( p^2 - 1 \) is not even.
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