Then by definition of we have .
Now what does injectivity tell us?
Suppose f: A--> B and let C be a subset of A.
Prove: if f is injective, then f^(-1)[f(C)] = C
I know from a previous theorem that C is a subset of f^(-1)[f(C)] so need only to prove f^(-1)[f(C)] is a subset of C.
So far I have:
Let f be injective. Let x be an element of f^(-1)[f(C)] . Then f(x) is an element of f(C).