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Math Help - Proving Sets

  1. #1
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    Exclamation Proving Sets

    Hey guys. I posted this yesterday. http://www.mathhelpforum.com/math-he...rs-184242.html. And got infractions, so it was a lesson.

    But now that this homework is done. Can you now teach me how to solve this thing? I got squat yesterday, I did not pass anything. So, now I want to know how to solve it. 'Cause the Prof. just let us submit the homework and he dismissed us after. He did not explain/teach us how to do it and what is the right answer.

    Please guys, it's no homework anymore, so please help me.
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  2. #2
    MHF Contributor

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    Re: Proving Sets

    Please tell us what you did.
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  3. #3
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    Re: Proving Sets

    Hello, edriann!

    \text{Prove:}

    n(A\cup B\cup C)
    . . . . =\:n(A) + n(B) + n(C) - b(A\cap B) - n(A\cap C) - n(B\cap C ) + n(A\cap B\cap C)

    We know the formula for two sets:
    . . n(P \cup Q) \:=\:n(P) + n(Q) - n(P\cap Q)


    We are given: A \cup B\cup C

    Group them into two sets: . A \cup [B \cup C]


    Then we have:

    n(A\cup [B \cup C]) \;=\;n(A) + n(B\cup C) - n(A \cap[B \cup C])

    . . =\;n(A) + n(B) + n(C) - n(B \cap C) - n([A\cap B]\cup[A\cap C])

    . . =\;n(A) + n(B) + n(C) - n(B \cap C)
    . . . .  - \bigg[n(A\cap B) + n(A\cap C) - n([A\cap B] \cap[A\cap C]\bigg]

    . . =\;n(A) + n(B) + n(C) - n(B\cap C) - n(A \cap B) - n(A\cap C) + n(A\cap B\cap C)

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