Let A and B be nonempty sets such that B \subset A. Prove that |A-B| <= |A|.   My proof:  Define f:A-B -> A such that f(a) = a. Let m,n \in A-B such that f(m) = f(n). Then by definition of f, m = n. <- this implies |A - B| <= |A|.   Is this correct?

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