Under what conditions is f one-to-one

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Let X be a set, and let A A⊂X. Define f: P(x)-> P(x) by f(B)=A∩B. Under what conditions is f one-to-one? Surjective? Here P(x) is the power set of X (i.e. the set of all subsets of X).

Reference no: EM131227942

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Under what conditions is f one-to-one : Let X be a set, and let A A⊂X. Define f: P(x)-> P(x) by f(B)=A∩B. Under what conditions is f one-to-one? Surjective? Here P(x) is the power set of X (i.e. the set of all subsets of X).
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