two short questions

1. $\displaystyle A=\left\{\left\{1\right\},\left\{1,2\right\}\right \},B=\left\{\left\{1\right\},\left\{2\right\}\righ t\}$

Now is this right? $\displaystyle A \cap B=\left\{\left\{1\right\}\right\} $?

2. Why does this hold: $\displaystyle f(A \cap B) \subset f(A) $

I know that $\displaystyle A \cap B $ is a subset of A and B. But why does this hold, when we have a function?

thanks for the help