My Math Forum sets theroy question

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 April 1st, 2010, 08:55 PM #1 Newbie   Joined: Jan 2009 Posts: 7 Thanks: 0 sets theroy question could someone help me with the proof of following in the sets theory A?(B?C) = (A?B)?C
 April 2nd, 2010, 05:25 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: sets theroy question What does the delta mean?
 April 2nd, 2010, 05:29 AM #3 Senior Member   Joined: Nov 2008 Posts: 199 Thanks: 0 Re: sets theroy question Ok, I'm going to write s instead of $\triangle$. x in As(BsC) iff either 1) x in A and x not in BsC or 2) x in BsC and x notin A. suppose 1). Then as x not in BsC either a) x not in B or C, or b) x in B and C. If a) then x in AsB and x not in C. If b) then x in C and x not in AsB. Either way x in (AsB)sC. To complete the proof you need to work out what happens when 2) holds and then use a similar method to show the inclusion the other way. p.s. $\triangle$ is the symmetric difference. $x\in A\triangle B \text{ iff } x\in A\setminus B\text{ or } x\in B\setminus A$.
 April 3rd, 2010, 02:46 AM #4 Newbie   Joined: Jan 2009 Posts: 7 Thanks: 0 Re: sets theroy question thanks alot

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