If f : P Q is onto (f[P] = Q), and X is a partition...

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If f : P → Q is onto (f[P] = Q), and X is a partition of Q. Let Y = {f-1 [x] | X E X). Prove that Y is a partition of P. Why did you need to assume that f is onto (or did you really need to assume that?). If f : P → Q is onto (f[P] = Q), and X is a partition of Q. Let Y = {f-1 [x] | X E X). Prove that Y is a partition of P. Why did you need to assume that f is onto (or did you really need to assume that?).

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To prove that Y is a partition of P we need to show two things 1 Y is a collection of nonempty subsets of P and 2 the subsets in are pairwise disjoint ... View the full answer