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Let f: A → B be a function, and let {Bi: i ∈ I} be...

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Advance Math

Let f: A → B be a function, and let {Bi: i ∈ I} be a partitionof B. Prove that {f−1(Bi): i ∈ I} is a partition of A. If~I is the equivalence relation corresponding to thepartition of B, describe the equivalence relation corresponding tothe partition of A. [REMARK: For any C ⊆ B, f−1C) = {x ∈ A: f(x) ∈C}.]

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