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Math Help - Another Proof by Induction

  1. #1
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    Another Proof by Induction

    So A ∪ B = A + B − A ∩ B
    A ∪ B ∪ C = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)

    So i see where this is going...
    Now to prove by induction how would i start?
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  2. #2
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    Re: Another Proof by Induction

    start by assigning a natural number to something. i suggest calling your sets \{A_j : j\in \{1,2,\dots, k\}\} and using induction on k.

    that is, you are doing induction on "the number of sets you are taking the union of". your base case is k = 2, although you have also listed k=3.

    one hopes you have previously established that (A U B) U C = A U (B U C), so that A U B U C is unambiguous.
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