Set theory proof

  • Thread starter hmph
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  • #1
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Main Question or Discussion Point

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.

Thanks
 

Answers and Replies

  • #2
haruspex
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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.
 
  • #3
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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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