Prove or disprove: If a relation is symmetric and transitive, then it is also reflexive. Define a relation R on Z by declaring that xRy if and only if x² = y² (mod 4). Prove that R is reflexive, symmetric and transitive.
Prove or disprove: If a relation is symmetric and transitive, then it is also reflexive. Define a relation R on Z by declaring that xRy if and only if x² = y² (mod 4). Prove that R is reflexive, symmetric and transitive.
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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Transcribed Image Text:15. Prove or disprove: If a relation is symmetric and transitive, then it is also
reflexive.
16. Define a relation R on Z by declaring that xRy if and only if x² = y² (mod 4).
Prove that R is reflexive, symmetric and transitive.
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