Proofs. Need help proving the following

Can anyone prove this?If S is a subset of D(f) then S is a subset of f^(-1)(f(S))

So far I have:

Let x be an element of S

Therefore, f(x) is an element of f(s)

f inverse of f(s) = {p is an element of D(f) | f(p) is an element of f(s)}

since f(x) is an element of f(s), then x is an element of f inverse f(s)

Anything else I can add or omit?

Any help is very much appreciated!

Re: Proofs. Need help proving the following

Quote:

Originally Posted by

**duckyone** [COLOR=#373737][FONT=Lucida Grande]Can anyone prove this?If S is a subset of D(f) then S is a subset of f^(-1)(f(S))

It is hard for to read your question. But I think it means:

If $\displaystyle f:A\to B$ and $\displaystyle S\subseteq A$ then $\displaystyle S\subseteq f^{-1}[f(S)]~.$.

The definition gives us $\displaystyle t\in S$ implies $\displaystyle f(t)\in f(S)$.

Can you finish?