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(a) Define the following terms: (i) Cartesian product of two sets; (ii) relation on a set X. (b) Write down a relation on the set {1,2,3} which is reflexive and symmetric but not transitive. (c) Let S be the relation on the set R \ {0} defined by xSy if and only if y/x € Q.

(a) Define the following terms: (i) Cartesian product of two sets; (ii) relation on a set X. (b) Write down a relation on the set {1,2,3} which is reflexive and symmetric but not transitive. (c) Let S be the relation on the set R \ {0} defined by xSy if and only if y/x € Q.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...
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(a) Define the following terms: (i) Cartesian product of two sets; (ii) relation on a set X. (b) Write down a relation on the set {1,2,3} which is reflexive and symmetric but not transitive. (c) Let S be the relation on the set R \ {0} defined by xSy if and only if y/x € Q. Prove that S is an equivalence relation.
Transcribed Image Text:(a) Define the following terms: (i) Cartesian product of two sets; (ii) relation on a set X. (b) Write down a relation on the set {1,2,3} which is reflexive and symmetric but not transitive. (c) Let S be the relation on the set R \ {0} defined by xSy if and only if y/x € Q. Prove that S is an equivalence relation.
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