Assignment 3 Solutions - Set Theory (MAT2000) - Math 2000:...

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Math 2000: Set TheoryAssignment 3Due Date: Oct. 1 2012Problem 1.LetA, B, Cbe sets. Determine if the following assertions are true or false. Provide a proof orcounterexample in each case.a)(AB)(BC)ABb)(AB)(BC)ABProof.a) False. Take as counterexampleA={a,1,2,3},B={b,1,2,3,4,5},C={c,1,2,3,4,5}. Workthrough why this fails. Of course there are other counterexamples,.b) False. Take as counterexampleA={1,2,3},B={a, b, c},C={0,1,2,3,4}. Work through why thisfails. Of course there are other counterexamples,.Problem 2.LetA, B, Cbe subsets ofU. ProveA(BC) = (AB)(AC).
Problem 3.LetA,B, andCbe sets in some universeU.Prove thatA(BΔC) = (AB)Δ(AC)by showing thatA(BΔC)and(AB)Δ(AC)are subsets of each other.Proof.SupposexA(BΔC). ThenxAandxBΔC, soxA,x(BC), andx /BC. So ifxBthenx /C, in which casexABandx /AC, sox(AB)(AC

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Term
Spring
Professor
Ashlock
Tags
Set Theory, Sets, Drink Coffee

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