# two short questions

• Sep 28th 2008, 06:09 AM
kuntah
two short questions
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
• Sep 28th 2008, 06:38 AM
Plato
Quote:

Originally Posted by kuntah
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? $\displaystyle A \cap B=\left\{\left\{1\right\}\right\}$?

Yes that is correct.

Quote:

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

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