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
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Author:Jerome E. Kaufmann, Karen L. Schwitters
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Chapter8: Functions
Section8.1: Concept Of A Function
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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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