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Set theory proof

  1. Aug 19, 2012 #1
    Hi, I have been trying for a very long time to prove the following set theory identity

    (A union B) intersect (B union C) intersect (C union A) = (A intersect B) union (B intersect C) union (C intersect A).

    I thought that I could simplify (A U B) intersect (B U C) intersect (C U A)
    as [B U (A intersect C) ]intersect (C U A), but venn diagrams show that this is not correct.

  2. jcsd
  3. Aug 19, 2012 #2


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    Do you know how to distribute union over intersection and vice versa?
    (AuB)^(BuC) = (A^(BuC))u(B^(BuC))
    Since B^(BuC) = B you can simplify that a little.
    Just keep applying those rules and the result should drop out.
    If you get stuck, post your working so far.
  4. Aug 21, 2012 #3
    Thank you, it worked. I probably did it in a more convoluted manner than required, but I was able to do it in around 12 lines.

    I didn't realise that you could distribute like that at first.
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