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Math Help - Family of sets.

  1. #1
    Super Member Deadstar's Avatar
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    Family of sets.

    For the following four properties of set algebra, write down what they reduce to for a family of just two sets;

    B \cap \bigcup_{\lambda \in \Lambda} A_{\lambda} = \bigcup_{\lambda \in \Lambda}(B \cap A_{\lambda})

    B \cup \bigcap_{\lambda \in \Lambda} A_{\lambda} = \bigcap_{\lambda \in \Lambda}(B \cup A_{\lambda})

    \left(\bigcup_{\lambda \in \Lambda}A_{\lambda}\right)' = \bigcap_{\lambda \in \Lambda}A'_{\lambda}

    \left(\bigcap_{\lambda \in \Lambda}A_{\lambda}\right)' = \bigcup_{\lambda \in \Lambda}A'_{\lambda}

    I'm not entirely sure what the \bigcap \bigcup symbols mean so if my workings wrong that's probably why. I don't want the answer, just someone to say whether this is right so far.

    For the first two... It reduces to;

    B \cap (A_1 \cup A_2) = (B \cap A_1)\cup(B \cap A_2)

    And

    B \cup (A_1 \cap A_2) = (B \cup A_1)\cap(B \cup A_2)

    Right so far?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Deadstar View Post
    Right so far?
    Yes, right so far!
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