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Math Help - Family of subsets

  1. #1
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    Family of subsets

    Prove: If  A \rightarrow B is a function and {  C_\lambda \mid \lambda \epsilon \Lambda } is a family of subsets of A, then  f ( \bigcup_{\lambda \epsilon \Lambda} C_\lambda) = \bigcup_{\lambda \epsilon \Lambda} f (C_\lambda)
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  2. #2
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    Quote Originally Posted by tigergirl View Post
    Prove: If  A \rightarrow B is a function and {  C_\lambda \mid \lambda \epsilon \Lambda } is a family of subsets of A, then  f ( \bigcup_{\lambda \epsilon \Lambda} C_\lambda) = \bigcup_{\lambda \epsilon \Lambda} f (C_\lambda)
    You need to show some of your own effort.
    Answer these two questions:
    1) What does it mean to say s \in f\left( {\bigcup\limits_{\lambda  \in \Lambda } {C_\lambda  } } \right)?

    2) What does it mean to say t \in \bigcup\limits_{\lambda  \in \Lambda } {f(C_\lambda  )}?
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  3. #3
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    Basically, the problem is to show that f(C_1\cup C_2)=f(C_1)\cup f(C_2). Both inclusions are pretty obvious. I don't think the extension to infinite families \Lambda (from \Lambda=\{1,2\} just considered) presents any problems.
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