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October 3rd, 2013, 02:32 PM  #1 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Are there any other methods to prove logical equivalence?
I can do that by using a truth table. But are there any other shorter ways of doing that?

October 3rd, 2013, 04:08 PM  #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: Are there any other methods to prove logical equivalence
Sure, you could transform the two by tautologies until they are (symbolically) equal.

October 3rd, 2013, 06:51 PM  #3 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Re: Are there any other methods to prove logical equivalence
Well, how do you know when to stop trying to transform them? I mean, when can you say 'NO, they aren't equivalent'. Because for long expressions it could take a while before you are out of transformation possibilities... and sometimes you will never be. Because I have this P ? (Q ? R) (P ? Q) ? (P ? R) by using a truth table they are not! 
October 3rd, 2013, 07:00 PM  #4 
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: Are there any other methods to prove logical equivalence
You can prove that they are inequivalent by finding an assignment which makes one true and the other false. (Essentially, you only need one row of the truth table as long as it's the right row.)

October 7th, 2013, 06:27 AM  #5  
Newbie Joined: Mar 2012 Posts: 25 Thanks: 0  Re: Are there any other methods to prove logical equivalence Quote:
A&B + A&C + B&D ... etc. So transform both expressions into that form and then compare the two.  
October 7th, 2013, 02:57 PM  #6  
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: Are there any other methods to prove logical equivalence Quote:
 

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