homework3 - LOGIC AND PROOF HOMEWORK 3 1. 1.5.3 (part f) 2....

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Unformatted text preview: LOGIC AND PROOF HOMEWORK 3 1. 1.5.3 (part f) 2. Suppose x is a real number such that x > ‐1. Prove by contraposition that x3 – x > 0. 3. 1.5.6 (part d) 4. Prove by contradiction that if a and b are integers, then a2 – 4b – 2 0. 5. Prove that for every integer n, 6 divides n if and only if 2 divides n and 3 divides n. 6. Prove that for every integer n, n3 is even if and only if n is even. 7. 1.5.8 8. Prove that there are infinitely many prime numbers. ...
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