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Topic: Need help w/ problem
Replies: 3   Last Post: Sep 26, 2012 2:45 AM

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Jon Awbrey

Posts: 36
Registered: 12/10/04
Re: Need help w/ problem
Posted: Sep 25, 2012 12:00 AM
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Alex,

To show ¬p V ¬q V ¬r = ¬p V (r -> ¬q)

Probably the easiest way to see that the two sides are equivalent
is to use the definition of x -> y as ¬x V y

That makes (r -> ¬q) = (¬r V ¬q)

So ¬p V (r -> ¬q) = ¬p V ¬r V ¬q

Jon

> Alex,
> Some true logic wonks watch this site. From an amateur's standpoint, two different ideas may be useful: (1) Write up "truth tables" for the two propositions. To say they're equivalent is precisely to say that the truth value of the propositions is the same for each choice of "T or F" for p, q and r; (2) Show that assuming the first is false forces the second to be false, and vice versa. That sounds different from saying that the truth of the first implies the truth of the second and vice versa; but the result is the same, since showing p implies q is equivalent to showing that ~q implies ~p.
> As mentioned above, you should get considerably more high-powered advice from some pro logicians on here. It's your decision what to use for your class. Thanks for a great problem!
> Ben
>
>

>> Date: Mon, 24 Sep 2012 13:57:29 -0400
>> From: discussions@mathforum.org
>> To: discretemath@mathforum.org
>> Subject: Need help w/ problem
>>
>> Hi all, back at math after a couple years break (even though I dont think the math I took would help with this). Anyway I'm just starting out with propositional equivalences and i needed help with this more intermediate problem. Any help would be greatly appreciated :)
>> Show that the compound propositions
>> ¬p V ¬q V ¬r and ¬p V (r -> ¬q)
>> are equivalent.

>


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