11-07-homework-5 - , the transitive closure of R . 4...

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Sets and Logic — Fall 2011 due Monday, 10/14/11 Homework #5 1 Suppose that R and S are partial orders on A . Is it true that R S is a partial order? Give a proof or counterexample. 2 Suppose that R and S are partial orders on A . Is it true that R S is a partial order? Give a proof or counterexample. 3 Let P be the set of all people who have ever lived, and deFne R = { ( p,q ) P × P | p is a parent of q } . Describe in words, not symbols
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Unformatted text preview: , the transitive closure of R . 4 Suppose that R is a relation on A , and let S denote the transitive closure of R . Prove that if R is symmetric, then so is S . 5 Let A be a set and B a subset of A . DeFne the relation R on P ( A ) by R = { ( X,Y ) ∈ P ( A ) × P ( A ) | ( X Δ Y ) ⊆ B } . Prove that R is an equivalence relation....
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This note was uploaded on 12/10/2011 for the course MHF 3202 taught by Professor Larson during the Fall '09 term at University of Florida.

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