Answered: Let S be the relation on the set R^2…

Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or disprove: the relation S 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 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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Question

Let S be the relation on the set R^2 defined by
(x, y) S (w, z) if |x| + |y| = |w| + |z|.
Prove or disprove: the relation S is an equivalence relation.

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