Recall that binary relations are merely sets of pairs of elements of some set. Therefore if R and Q are binary relations on a same set A, their union R ∪ Q as sets of pairs is also a binary relation on A. Is it true that if R and Q are antisymmetric then R ∪ Q is also antisymmetric? Prove that it is or give a counterexample.

Recall that binary relations are merely sets of pairs of elements of some set. Therefore if R and Q are binary relations on a same set A, their union R ∪ Q as sets of pairs is also a binary relation on A. Is it true that if R and Q are antisymmetric then R ∪ Q is also antisymmetric? Prove that it is or give a counterexample.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6E: In Exercises 610, a relation R is defined on the set Z of all integers, In each case, prove that R...

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