Let f: A B. If {B1, B2, B3, . . . , Bn} is a partition

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Let f: A → B. If {B1, B2, B3, . . . , Bn} is a partition of B, prove that {f-1(Bt) | l ≤ i ≤ n, f-l(Bt) ≠ ∅} is a partition of A.
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