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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...a,b},{a,c},{b,c},{a,b,c}].

Now, we know a function or mapping is one-to-one, if for all x1 and x2 that are elements of the set, ...