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Thread: two short questions

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by kuntah View Post
    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 View Post
    2. Why does this hold: $\displaystyle f(A \cap B) \subset f(A) $
    $\displaystyle \begin{gathered} A \cap B \subseteq A \hfill \\ x \in A \cap B \Rightarrow f(x) \in f(A \cap B) \wedge f(x) \in f(A) \hfill \\ \end{gathered}$
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