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# HW6 - on S Justify your answer 3(3 points Suppose that S is...

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Math 100 Homework 6 Martin H. Weissman 1. (3 points) Let R be the following relation on the set R : R = { ( x,y ) R 2 such that | x - y | ≤ 1 } . Is this relation reﬂexive? Symmetric? Transitive? Anti-symmetric? If your answer is yes, prove it. If your answer is no, give a counterexample. 2. (2 points) Let S be a set with four elements. How many equivalence relations are there
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Unformatted text preview: on S ? Justify your answer. 3. (3 points) Suppose that S is a set. Let R 1 and R 2 be two relations on S . Let R = R 1 ∩ R 2 . Prove that if R 1 is symmetric and R 2 is symmetric, then R is symmetric. Prove that if R 1 is transitive, and R 2 is transitive, then R is transitive....
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