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Math Help - two short questions

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by kuntah View Post
    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.

    Quote Originally Posted by kuntah View Post
    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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