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okay I have an equivalence that I have to prove. these equivalences use biconditionals and boolean algebra. but I'm not sure which order I apply the laws of logical equivalence.

EDIT:

It is an assignment. I've been stuck on it for days getting different answers different times.

-(p V (q ^ -r)) ^ q == (-p ^ q) ^ r

I don't necessarily want anyone to solve it, I want them to explain, in a generic way, how they would go about solving it and the order they apply the laws. that way I can learn from it.

Kjuly
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andrew Patterson
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    We can't help much without knowing the actual problem you are trying to solve. Also this sounds like homework. Make sure you include your attempts to solve the problem, what Google told you, what specifically you don't understand, etc. – benekastah Oct 17 '12 at 16:22

2 Answers2

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Well there's only so many equivalencies to go around. Through these kinds of classes and mathematics ones too, commonly you didn't have but a few tricks in the toolbox so to speak. De Morgans laws, etc. A chapter might mention like 4-5 rules and you should definitely try all of those.

Might help to work from the opposite side too if you've only been working the equation in one direction. It's very much a play around with it until you get enough experience to identify a better initial guess. But as you play with it you'll start to see a few manipulations to get reasonably close and then the problem solving comes in to figure out the 1-2 manipulations left you aren't seeing. Even my best professors told me you have to beat your head on a desk til it works.

user1701047
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  • ah ok, i feel I may have got the answer correct, but i'll work it backwards and check the result against a truth table for each stage of the mainipulating(that will work right?) thanks anyway! – andrew Patterson Oct 17 '12 at 17:23
  • great you got it ;D. You should just be able to apply everything you did in reverse as well. I don't know what the problem was or what you did exactly. If you do the truth tables correctly, they should of course be equivalent--it might be a lot to write out though! – user1701047 Oct 17 '12 at 17:37
  • well its an assessment, so I'm gonna make sure I get it right haha. I reckon what I was doing was applying the laws in the wrong order, therefore the operators were not used in order of precedence. I think anyways... – andrew Patterson Oct 17 '12 at 17:47
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-(p V (q ^ -r)) ^ q

-((p V q) ^ (p V -r)) ^ q [by distr of V over ^]

(-(p V q) V -(p V -r)) ^ q [by DeMorgan]

((-p ^ -q) V (-p ^ r)) ^ q [by DeMorgan]

(-p ^ -q) ^ q V (-p ^ r) ^ q [by distr of V over ^]

-p ^ (-q ^ q) V (-p ^ r) ^ q [by assoc of ^]

-p ^ F V (-p ^ r) ^ q [by A ^ -A == F, where F is falsity (0)]

F V (-p ^ r) ^ q [by A ^ F == F, where F is falsity (0)]

(-p ^ q) ^ r [by A v F == A, where F is falsity (0)]

carmelo anthony
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