Let A and B be two nonempty sets, f: A → B be a function and R be an equivalence relation on the set B. For r1, c2 E A, we put xRx2 if and only if f(x1)Rf(x2). Show that R' is an equivalence relation on the set A.
Let A and B be two nonempty sets, f: A → B be a function and R be an equivalence relation on the set B. For r1, c2 E A, we put xRx2 if and only if f(x1)Rf(x2). Show that R' is an equivalence relation on the set A.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 18E: Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on...
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