Problem 6 Let A and B be sets, and let f: A → B be a function. Let ∼ be the relation on A defined by x ∼ y if and only if f (x) = f (y), for all x, y ∈A. Prove that ∼ is an equivalence relation.
Problem 6 Let A and B be sets, and let f: A → B be a function. Let ∼ be the relation on A defined by x ∼ y if and only if f (x) = f (y), for all x, y ∈A. Prove that ∼ is an equivalence relation.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.1: Concept Of A Function
Problem 100PS
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Problem 6
Let A and B be sets, and let f: A → B be a function. Let ∼ be the relation on A
defined by x ∼ y if and only if f (x) = f (y), for all x, y ∈A. Prove that ∼ is an equivalence
relation.
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