2. Let ƒ : A → B be a function, and ~ an equivalence relation on B. For a₁, a2 € A, we say a₁ ≈ a2 if ƒ(a₁) ~ f(a₂). Prove that ≈ is an equivalence relation.

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter3: Graphs And Functions
Section3.5: Relations And Functions
Problem 335E: Is every relation a function? Is every function a relation?
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2. Let ƒ : A → B be a function, and ~ an equivalence relation on B. For
≈
a1, a2 € A, we say a₁ a₂ if f(a₁)~ f(a₂). Prove that is an equivalence
≈
relation.
Transcribed Image Text:2. Let ƒ : A → B be a function, and ~ an equivalence relation on B. For ≈ a1, a2 € A, we say a₁ a₂ if f(a₁)~ f(a₂). Prove that is an equivalence ≈ relation.
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