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Math Help - Another set proof

  1. #1
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    Another set proof

    Prove:

    P{(AuB)nC} = P{AnC} + P{BnC} - P{AnBnC}

    u denotes union
    n denotes intersection


    Here is what I have so far. (To prove I'm not just posting questions without trying.) I'm probably in the completely wrong direction.

    P{(AuB)nC} = P(A) + P(B) + P(C) - P(AuBuC)
    P{(AuB)nC} = P(AuB) + P(AnB) + P(C) - P(AuBuC)
    P{(AuC)n(BuC)} = P(AuB) + P(AnB) + P(C) - P(AuBuC)
    P(AuB) + P(AnB) + P(C) = -p(AuBuC) - P{(AuC)n(BuC)}
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  2. #2
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    To do these you need to know basic set theory.
    P\left( {\left[ {A \cup B} \right] \cap C} \right) = P\left( {\left[ {A \cap C} \right] \cup \left[ {B \cap C} \right]} \right) = P\left( {\left[ {A \cap C} \right]} \right) + P\left( {\left[ {B \cap C} \right]} \right) - P\left( {\left[ {A \cap C} \right] \cap \left[ {B \cap C} \right]} \right)
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  3. #3
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    See, that third step comes out of nowhere for me. Is there somewhere I can find these rules? I've never seen sets before in my life (don't know why), so this is all completely new to me.
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  4. #4
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    Quote Originally Posted by ban26ana View Post
    Is there somewhere I can find these rules? I've never seen sets before in my life (don't know why), so this is all completely new to me.
    If that is true then there is absolutely no reason for you to have been placed in a course that requires these proofs. You need to make your academic advisor aware of this situation. If you are in a course that does require these proofs, then you should consider taking first a course in foundations(set theory). That is where you will find these ideas.
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