Let $f: A \rightarrow B$, $D \subseteq A$, and $E \subseteq B$. Prove that $f^{-1}(B - E) \subseteq A - f^{-1}(E)$

Question

Proof: Let $x \in f^{-1}(B-E)$, then $x \in f^{-1}(B)$ and $x \notin f^{-1}(E)$... ...

I know I want to show that $x \in A - f^{-1}(E)$, but how can I show that $x \in A$?

what about $D$? why did u mention it at all? – Fibo Kowalsky Nov 22 '13 at 01:58 — Fibo Kowalsky, Nov 22 '13 at 01:58
See also http://math.stackexchange.com/q/553306/11994. – MarnixKlooster ReinstateMonica Nov 22 '13 at 07:04 — MarnixKlooster ReinstateMonica, Nov 22 '13 at 07:04

score 0 · Accepted Answer · answered Nov 22 '13 at 01:56

0

Hint: $A$ is the domain of $f$. If it's anywhere, it's in there.

Also, a stronger result is true: $f^{-1}(B\setminus E)=f^{-1}(B)\setminus f^{-1}(E)$.

answered Nov 22 '13 at 01:56

Hayden

1 Answers1