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1. Prove that the difference of two odd integers is even. Give a justification at each step.
2. Prove that the sum of any two rational numbers is a rational number. Give a justification at each step.
3. Prove by contradiction that there is no greatest integer.
4. Prove by contraposition that for all integers n, if n2 is even then n is even.
5. Prove using mathematical induction: ∀ integers n ≥ 1, 2 + 4 + ... + 2n = n2 + n. Give justifications for each step.
6. Explain the difference between proof by contradiction and proof by contraposition. Give an example of a theorem that would lend itself to proof by contradiction. Explain why that proof technique would be a good choice in this case.
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