A = {1, 3, 7, 9} and S be the binary relation on A defined by: x S y <=> x^3 ≡ y (mod 10) (a) State explicitly which ordered pairs are in S. (b) State explicitly which ordered pairs are in S^-1. (c) Is S reflexive? Yes or No? (circle one, no proofs.) (d) Is S symmetric? Yes or No? (circle one, no proofs.) (e) Is S transitive? Yes or No? (circle one, no proofs.)

A = {1, 3, 7, 9} and S be the binary relation on A defined by: x S y <=> x^3 ≡ y (mod 10) (a) State explicitly which ordered pairs are in S. (b) State explicitly which ordered pairs are in S^-1. (c) Is S reflexive? Yes or No? (circle one, no proofs.) (d) Is S symmetric? Yes or No? (circle one, no proofs.) (e) Is S transitive? Yes or No? (circle one, no proofs.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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