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I'm trying to prove that if f:X->Y and A & B are subsets of X, that f(A intersect B) is a subset of f(A) intersect f(B).

I started by trying to show set containment, beginning with an arbitrary element in f(A intersect B). However, I cannot figure out how to transition into the right hand side of the problem.

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The second question I have is proving that if A and B are finite sets having the same cardinality and f:A->B is one-to-one then f is onto.

I missed class this day and can't figure out what cardinality is by reading the chapter.

Someone please help! =\