Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN: 9781285463230
Author: Gilbert, Linda, Jimmie
Publisher: Cengage Learning,
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Let us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c or b = d. Is this relation (a) reflexive (b) symmetric (c) antisymmetric (d) transitive? Is this an equivalence relation
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Transcribed Image Text:Let us consider the following relation R on the set of all pairs of integers: (a,b)R(c,d) if a = c or b = d. Is this relation (a) reflexive (b) symmetric (c) antisymmetric (d) transitive? Is this an equivalence relation
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    Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
  • In Exercises , a relation is defined on the set of all integers. In each case, prove that is an equivalence relation. Find the distinct equivalence classes of and list at least four members of each. 10. if and only if .
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