two short questions

**kuntah** · September 28th 2008, 06:09 AM

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

**Plato** · September 28th 2008, 06:38 AM

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: $f(A \cap B) \subset f(A)$

$\begin{gathered} A \cap B \subseteq A \hfill \\ x \in A \cap B \Rightarrow f(x) \in f(A \cap B) \wedge f(x) \in f(A) \hfill \\ \end{gathered}$

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