hw4sol - CSE 20: Discrete Mathematics Fall 2010 Problem Set...

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Unformatted text preview: CSE 20: Discrete Mathematics Fall 2010 Problem Set 4 Instructor: Daniele Micciancio Due on: Wed. Nov 3, 2010 Problem 1 (6 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 ) : True 2. ( A \ C ) ( B \ C ) and ( A \ B ) are disjoint: True 3. ( A B ) C = A ( B C ) : False Problem 2 (5 points) Let A = { 1 , 3 } , B = { 5 , 6 } and C = { 1 , 3 , 5 , 7 , 9 } . List the elements for each of the following sets: 1. ( A B ) C = { 1 , 3 , 5 } 2. ( A B ) A = { (1 , 5) , (1 , 6) , (3 , 5) , (3 , 6) , 1 , 3 } 3. = 4. { x C | ( x + 1) A B } = { 5 } 5. ( C \ ( A B )) 2 = { (7 , 7) , (7 , 9) , (9 , 7) , (9 , 9) } Problem 3 (8 points) Let A and B be subsets of a universal set U . Use the definition of the set operations (as given in class an in section 2.2 of the textbook) and the rules of logic to prove the following identity: ( A B ) ( A B ) = ( A B ) ( A B ) Proof: Let x be an arbitrary element, and define the predicates P ( x ) = x A and Q ( x ) = x B ....
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This note was uploaded on 01/08/2011 for the course CSE cse105 taught by Professor Cs during the Fall '10 term at UCSD.

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hw4sol - CSE 20: Discrete Mathematics Fall 2010 Problem Set...

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