quiz3-review - , 1)]. Hint: what equation do you get if you...

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CS 173: Discrete Structures, Spring 2010 Quiz 3 review These problems should not be turned in. They are to help you review for the third quiz. 1. Relation properties A B C D Refexive : Irrefexive : Symmetric : Antisymmetric : Transitive : is the relation on R such that x y if and only if xy = 1 Refexive : Irrefexive : Symmetric : Antisymmetric : Transitive : A B C D E Refexive : Irrefexive : Symmetric : Antisymmetric : Transitive : 1
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2. Equivalence classes Let A = R + × R + - { (0 , 0) } , i.e. pairs of positive reals in which no more than one of the two numbers is zero. Consider the equivalence relation on A deFned by ( x, y ) ( p, q ) ( xy )( p + q ) = ( pq )( x + y ) (a) List four elements of [(3
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Unformatted text preview: , 1)]. Hint: what equation do you get if you set ( x, y ) to (3 , 1) and q = 2 p ? (b) Give two other distinct equivalence classes that are not equal to [(3 , 1)]. (c) Describe the members of [(0 , 4)]. 3. Graph isomorphism (a) Prove that the following two graphs are isomorphic. That is, for each vertex in G 1, give the corresponding vertex in G 2, making sure your mapping preserves the edge structure. G1: A B C D E G2: 1 5 3 4 2 (b) Prove that the following two graphs are not isomorphic. G1: A B C D E G2: 1 2 3 4 5 2...
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This note was uploaded on 11/09/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.

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quiz3-review - , 1)]. Hint: what equation do you get if you...

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