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Unformatted text preview: Answers to Homework 31 January 2008 13.1 Relations on A = f 1 ; 2 ; 3 ; 4 ; 5 g . (a) f (1 ; 1) ; (2 ; 2) ; (3 ; 3) ; (4 ; 4) ; (5 ; 5) g is the equality relation. It is re&ex ive, symmetric, antisymetric and transitive. (b) f (1 ; 2) ; (2 ; 3) ; (3 ; 4) ; (4 ; 5) g is the relation given by the equation y = x + 1 . It is irre&exive and antisymmetric. (c) f (1 ; 1) ; (1 ; 2) ; (1 ; 3) ; (1 ; 4) ; (1 ; 5) g is the relation given by the equation x = 1 . It is antisymmetric and transitive. (d) f (1 ; 1) ; (1 ; 2) ; (2 ; 1) ; (3 ; 4) ; (4 ; 3) g is symmetric. (e) f 1 ; 2 ; 3 ; 4 ; 5 g & f 1 ; 2 ; 3 ; 4 ; 5 g is re&exive, symmetric, and transitive. 13.2 R is a relation on the set Z of integers: xRy if x and y di/er by at most 2 . (a) R = f ( x;y ) : x and y are in Z , and j x ¡ y j ¢ 2 g . (b) R is re&exive because j x ¡ x j = 0 ¢ 2 for all integers x . (c) R is not irre&exive because, for example, j 3 ¡ 3 j = 0 ¢ 2 ....
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This note was uploaded on 07/13/2011 for the course MAD 2104 taught by Professor Staff during the Spring '08 term at FAU.
 Spring '08
 STAFF

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