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1. Use a direct proof to show that the sum of two even integers is even.
3. Show that the additive inverse, or negative, of an even number is an even number using a direct proof.
4. Use a direct proof to show that the product of two odd numbers is odd.
5. Prove that if n is a perfect square, then n + 2 is not a perfect square.
6. Use a direct proof to show that the product of two rational numbers is rational.
7. Prove that if m and n are integers and mn is even, then m is even or n is even.
8. Prove that if n is an integer and 3n + 2 is even, then n is even using
a) a proof by contraposition
b) a proof by contradiction
9. Prove the proposition P(1), where P(n) is the proposition “If n is a positive integer, then n2 ≥ n”. What kind of proof did you use?
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