Thread: Pre-Image / Image proof

I'm new to topology and have a pretty basic proof to perform but haven't had much experience with proofs and could use some help,

Question asks, to prove that if f: A -> B and X is a subset of A

prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X,

this makes perfect sense to me that it's true but i'm unsuer how to construct the proof any help would be appreciated, cheers.

Originally Posted by monster

Question asks, to prove that if f: A -> B and X is a subset of A prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X,

If then, . But by definition, , then, satisfies the condition for being in . As a consequence, .