# HW5 - B = 5 6 and C = 1 3 5 7 9 List the elements for each...

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CSE 20: Discrete Mathematics Spring 2010 Problem Set 5 Instructor: Daniele Micciancio Due on: Thu. May 20, 2010 Problem 1 (9 points) Let A,B and C be subsets of U . Prove or disprove each of the following statements using Venn diagrams: 1. ( A \ B ) \ C = A \ ( B C ) 2. ( A \ C ) ( B \ C ) and ( A \ B ) are disjoint 3. ( A B ) C = A ( B C ) Problem 2 (8 points) Remember the deﬁnition of set inclusion: A B if x.x A x B . Use the deﬁnition of , (strict inclusion, where A B is an abbreviation of ( A B ) ( A 6 = B ) ) and the rules of logic to prove the following statement: “If A B and B C , then A C ”. Problem 3 (5 points) Let A = { 1 , 3
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Unformatted text preview: } , B = { 5 , 6 } and C = { 1 , 3 , 5 , 7 , 9 } . List the elements for each of the following sets: 1. ( A ∪ B ) ∩ C 2. ( A × B ) ∪ A 3. ∅ × ∅ 4. { x ∈ C | ( x + 1) ∈ A ∪ B } 5. ( C \ ( A ∪ B )) 2 Problem 4 (8 points) Use the algebraic rules for sets given in Theorem 1 (pages 82-83, SF2-SF3 of the textbook) to prove the following equalities: 1. ( A ∩ B c ) ∩ C c = A ∩ ( B ∪ C ) c 2. ( A ∩ B ) ∪ ( A c ∩ B c ) = ( A ∪ B c ) ∩ ( A ∩ B c ) c...
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## This note was uploaded on 09/24/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.

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