Define a relation Q on the set R × R as follows. For all ordered pairs (w, x) and (y, z) in R x R, (w, x) Q (y, z) = x = z. (a) Prove that Q is an equivalence relation. To prove that Q is an equivalence relation, it is necessary to show that Q is reflexive, symmetric, and transitive. Proof that Q is an equivalence relation:

Define a relation Q on the set R × R as follows. For all ordered pairs (w, x) and (y, z) in R x R, (w, x) Q (y, z) = x = z. (a) Prove that Q is an equivalence relation. To prove that Q is an equivalence relation, it is necessary to show that Q is reflexive, symmetric, and transitive. Proof that Q is an equivalence relation:

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 22E: A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which...

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