# Thread: Is this proof correct?

1. ## Is this proof correct?

Let f: A -> B and X be subsets of A.

Prove: X is a subset of f inverse of f(X)

Let b be in f(X) which implies b=f(a) where a is in X
f inverse of b=f inverse of f(a)=a which implies f inverse of b is in X
which implies X is a subset of f inverse of f(X)

qed

Did I do this correctly?

Thanks!

2. Originally Posted by economanc
Let f: A -> B and X be subsets of A.

Prove: X is a subset of f inverse of f(X)

Let b be in f(X) which implies b=f(a) where a is in X
f inverse of b=f inverse of f(a)=a which implies f inverse of b is in X
which implies X is a subset of f inverse of f(X)

qed

Did I do this correctly?

Thanks!
Hi economanc.

The correct way is to start by letting $a$ be in $X$ and then proceed to show that $a$ is in $f^{-1}\left(f(X)\right).$