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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Let \( f : A \to B \) be a function, and \(\sim\) an equivalence relation on \( B \). For \( a_1, a_2 \in A \), we say \( a_1 \approx a_2 \) if \( f(a_1) \sim f(a_2) \). Prove that \(\approx\) is an equivalence relation.
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