homework4 - LOGIC AND PROOF HOMEWORK 4 1. 2.1.7 2. Prove...

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Unformatted text preview: LOGIC AND PROOF HOMEWORK 4 1. 2.1.7 2. Prove that (A B) = (A) (B) for all sets A and B. [Hint: Use Theorem 2.2.1] 3. Prove that (A) (B) (A B), and show by example that the converse is not true. [Hint: Use Theorem 2.2.1] 4. Prove that C – (A B) = (C – A) (C – B) for all sets A, B, and C. 5. Provide a counterexample to show that A – (B – C) = (A – B) – C is not true. 6. Is it true that (A – B)C = AC – BC? Prove or provide a counterexample. 7. 2.3.1 (part d) 8. For each nℕ let An = Find and , . . How would your answers change if the intervals were closed instead of open? ...
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