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Question
Let P be the power set of {a,b,c}. A function f: P-->Z;the set of integers, follows: For A in P, f(A)=the number of elements in A.
1. Is f one-to-one?
2. Is f onto?

...thank you very much in advance!

Answer
I suggest you list all the elements of the power set of {a,b,c} (there are eight of them which includes the empty set.) Notice that you are juts listing all the possible subsets. Next to each set A write down f(A) which is the number of elements in A. For example f of the empty set is 0, f of {a,b,c} is 3. I suspect you will quickly answer your questions.

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