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Question about One-to-one functions

Define F: power P({a, b, c}) -> Z as follows: for all A exist in power P({a, b, c}), F(A) = the number of elements in A. a). Is F one-to-one? Please give proof or give a counterexample. Please explain so I may understand. Thanks

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Given a set S, the power set of S is the set of all subsets of S. In the case of the set {a,b,c}, the power set is ...

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This is a proof regarding a one-to-one function.

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