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Math Help - Proof by induction A u B = A + B - A n B

  1. #1
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    Proof by induction A u B = A + B - A n B

    So for the union of A1 and A2 .. A1 u A2 = A1 + A2 - A1 n A2

    Prove by induction that it is true for all Unions

    So i start with another Union A3 so,

    A1 u A2 u A3 = A1 + A2 +A3 - (A1 n A2) - (A1 n A3) - (A2 n A3) + (A1 n A2 n A3)

    now i want to to prove for n+1. or for all unions

    How would i do this?
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  2. #2
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    Re: Proof by induction A u B = A + B - A n B

    Quote Originally Posted by Aquameatwad View Post
    So for the union of A1 and A2 .. A1 u A2 = A1 + A2 - A1 n A2

    Prove by induction that it is true for all Unions

    So i start with another Union A3 so,

    A1 u A2 u A3 = A1 + A2 +A3 - (A1 n A2) - (A1 n A3) - (A2 n A3) + (A1 n A2 n A3)

    now i want to to prove for n+1. or for all unions

    How would i do this?
    Start by at least setting up an equation for \displaystyle A_1 \cup A_2 \cup A_3 \cup \dots \cup A_n that you want to prove...
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  3. #3
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    Re: Proof by induction A u B = A + B - A n B

    So,

    (UAi) = ∑Ai - ∑(Ai n Aj) + ∑(Ai n Aj n Ak ) + ... +∑(Ai n Aj ... Aq) - ∑(A1 n A2 .... n An)

    is this correct?
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