10-26-homework-4 - i A R . 4 Let R be a relation on A , and...

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Sets and Logic — Fall 2011 due Wednesday, 11/2/11 Homework #4 1 Suppose that R is a relation from S to T and S and T are both relations from B to C . Must it be true that ( S T ) R = ( S R ) ( T R )? Give a proof or a counterexample to justify your answer. 2 Suppose that R is a relation from S to T and S and T are both relations from B to C . Must it be true that ( S T ) R = ( S R ) ( T R )? Give a proof or a counterexample to justify your answer. 3 Let R be a relation on A . Prove that R is reFexive if and only if
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Unformatted text preview: i A R . 4 Let R be a relation on A , and dene P = P ( A ) \ {} ; in other words, P contains all nonempty subsets of A . Dene the relation S on P by S = { ( X,Y ) P P | for all x X and all y Y , xRy } . Prove if R is transitive, then S is transitive as well. 5 Why did we need to exclude the emptyset in the previous problem?...
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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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