October 9th, 2011, 10:19 AM  #1 
Joined: Oct 2011 Posts: 4 Thanks: 0  Simplifying Algebra Proposition
guys i seriously have no idea on how to start this one.. (pVq)^(pVq)^(pVq)^(pVq) how to simplify this one? my teacher gave me this example: p^(pVq) = (pVf)^(pVq) < how is that f in there?? = p V (f^q) = p V f = p i could just solve this using truth table, but he want me to use algebra rules. if you guys can help me, i would definitely appreciate it thanks alot im having problem with the rules of algebra being implemented in non numeric arguments. i did truth table of (pVq)^(pVq)^(pVq)^(pVq) and found that the whole proposition is equivalent to (pVq) 
October 9th, 2011, 04:19 PM  #2  
Joined: Jun 2011 Posts: 298 Thanks: 0  Re: Simplifying Algebra Proposition Quote:
Your teacher uses to denote the truth value of a false statement, which he meant a contradiction since a contradicting statement is false. I assume you know that the truth value of , and of . If you substitute for , you will get , and of , see[*] , see [**] Quote:
You do the rest.  
October 9th, 2011, 04:59 PM  #3 
Joined: Oct 2011 Posts: 4 Thanks: 0  Re: Simplifying Algebra Proposition
[ ((p ^ p) V q) ^ (p V q) ^ (p V q) ((p ^ p) V q) ^ ((p ^ p) V q) (F V q) ^ ((p ^ p) Vq) = (F V q = q) ^ ( (p ^ p = F) V q) = q ^ (F V q) = q ^q did i do it right? 
October 9th, 2011, 07:45 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,196 Thanks: 344  Re: Simplifying Algebra Proposition Hello, abang526! The statement is a selfcontradiction . . . always false. We need a couple of theorems: [color=beige]. . [/color] Quote:  
October 9th, 2011, 10:32 PM  #5 
Joined: Oct 2011 Posts: 4 Thanks: 0  Re: Simplifying Algebra Proposition
thanks soroban for your explanation.. so anyway, here's something i tried on my own.. (p^(pVq)) V q ^ (qVp) p ^ p ^ q V q < ( q ^ q V p = q right? ) f ^ q V q f V q T is it correct? thanks 
October 10th, 2011, 01:52 AM  #6 
Joined: Oct 2011 Posts: 4 Thanks: 0  Re: Simplifying Algebra Proposition
i dont mean to keep asking here, i do get the ideas but the methods are somehow different.. im totally lost on how to do the next one.. (p V ( q > p)) V ((p <> q) > (q ^ p)) (p ^ (q > r)) V ((p V r) <> q) (p ^ q) > ( p ^ r) V ((p V q) <> ( r V q)) < does it work like this? thanks a lot!! 
September 29th, 2013, 03:42 AM  #7 
Joined: Sep 2013 Posts: 1 Thanks: 0  Re: Simplifying Algebra Proposition
how to simplyfy this? (p'^q)\/('(p^q')^(p\/q')) 

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algebra, proposition, simplifying 
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