Abstract Algebra: Theory and Applications · Problem 1.13

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · equivalence-relations

Problem

Let f:A→Bf : A \to B be a map. Define a relation ∼\sim on AA by a1∼a2a_1 \sim a_2 if f(a1)=f(a2)f(a_1) = f(a_2). Prove that ∼\sim is an equivalence relation.

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