# Math Help - two short questions

1. ## two short questions

two short questions

1. $A=\left\{\left\{1\right\},\left\{1,2\right\}\right \},B=\left\{\left\{1\right\},\left\{2\right\}\righ t\}$
Now is this right? $A \cap B=\left\{\left\{1\right\}\right\}$?

2. Why does this hold: $f(A \cap B) \subset f(A)$
I know that $A \cap B$ is a subset of A and B. But why does this hold, when we have a function?

thanks for the help

2. Originally Posted by kuntah
1. $A=\left\{\left\{1\right\},\left\{1,2\right\}\right \},B=\left\{\left\{1\right\},\left\{2\right\}\righ t\}$
Now is this right? $A \cap B=\left\{\left\{1\right\}\right\}$?
Yes that is correct.

Originally Posted by kuntah
2. Why does this hold: $f(A \cap B) \subset f(A)$
$\begin{gathered} A \cap B \subseteq A \hfill \\ x \in A \cap B \Rightarrow f(x) \in f(A \cap B) \wedge f(x) \in f(A) \hfill \\ \end{gathered}$