Originally Posted by

**detalosi** Hey,

I want to show that $\displaystyle f(A\backslash B) \subset f(A) \backslash f(B)$

I have done the following:

Assume that $\displaystyle y \in f(A\backslash B)$.

This means that $\displaystyle \exists x\in A\backslash B: f(x)=y$ (by definition).

This means that $\displaystyle x\in A \land x\notin B$.

This means that $\displaystyle f(x) \in f(A) \land f(x) \notin B$.

This means that $\displaystyle f(x) \in f(A) \backslash f(B)$

Therefore $\displaystyle f(A\backslash B) \subset f(A) \backslash f(B)$.

Is the above correct?