homework6 - LOGIC AND PROOF HOMEWORK 6 1. Prove that (A x...

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Unformatted text preview: LOGIC AND PROOF HOMEWORK 6 1. Prove that (A x B) (C x D) = (A C) x (B D) for all sets A, B, C, and D. 2. Prove by counterexample that in general (A x B) (C x D) (A C) x (B D). 3. 3.2.5 (part a) 4. 3.2.5 (part g) 5. List the ordered pairs in the equivalence relation on A = { 1, 2, 3, 4, 5, 6} associated with the partition { {1, 2, 3}, {4, 5}, {6} }. 6. Describe the partition for the following equivalence relation: For x, y , x R y iff 3 divides x – y. 7. Define the relation R on x by (a, b) R (x, y) iff a < x or both a = x and b y. Prove that R is a partial ordering for x . 8. Find the supremum and infimum of the following two sets: i) { 1/n : n } ii) ⋂ 1 ,1 ...
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