February 25th, 2014, 05:31 PM  #1 
Newbie Joined: Feb 2014 Posts: 3 Thanks: 0  Simplify set expression
Good evening everyone. I'm new to discrete math, and I've been struggling with this problem for two days now. The problem is to simplify the following: ((B U C) ? (A  B) ? (B ? C' )' I used ` to denote complement, I couldn't find a symbol for it in character map. So I have been looking at this problem, and I made some progress with the set difference laws, DeMorgan's laws, and the double complement law, but I really can't seem to figure it out past that. I really appreciate any help that anyone can give me. 
February 25th, 2014, 05:32 PM  #2 
Newbie Joined: Feb 2014 Posts: 3 Thanks: 0  Re: Simplify set expression
Missed a ) in that, sorry: ((B U C) ? (A  B)) ? (B ? C' )' 
February 25th, 2014, 07:20 PM  #3  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Simplify set expression Quote:
A  B contains no elements from B, so neither can (B U C) ? (A  B) and hence this equals C ? (A  B). (B ? C' )' is B' U C by De Morgan's law, so the whole expression simplifies to (C ? (A  B)) ? (B' U C). But all elements on the left are in C, so this is just (C ? (A  B)) ? C = C ? (A  B). That's pretty much as simple as you can get, unless you want to replace  with its definition.  
February 26th, 2014, 01:04 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Simplify set expression Hello, Zyous! Quote:  
February 26th, 2014, 01:31 PM  #5 
Newbie Joined: Feb 2014 Posts: 3 Thanks: 0  Re: Simplify set expression
Wow thank you very much for the help! If I can bother you by asking the second part of the question, it would be very helpful. The second part is to see how the answer would change if the first question were instead ((B U C) ? (A  B)) ? (B' ? C)', with the compliment moved from the C to the B in at the end of the problem. Again, thanks a lot for the detailed answer, it's really helping me see how this process works! 
February 26th, 2014, 09:34 PM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Simplify set expression Hello, Zyous! Quote:  
February 27th, 2014, 02:02 AM  #7 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115  Re: Simplify set expression
Good stuff, although: 
February 27th, 2014, 02:52 AM  #8 
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Simplify set expression Absolutely correct, Pero! [color=beige]. . [/color](I must have had Logic on my mind.) I'll go back and correct them. 
March 12th, 2014, 05:55 AM  #9  
Guest Joined: Posts: n/a Thanks:  Re: Simplify set expression Quote:
 

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