2 Replies - 2330 Views - Last Post: 09 August 2012 - 03:53 AM

#1 TechSyndrome  Icon User is offline

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Check validity of argument - Propositional Logic

Posted 08 August 2012 - 07:19 PM

Hi. I've been given this exam question:


Describe how the validity of arguments can be checked using truth-tables. Illustrate your answer by checking whether each one of the following argu- ments is valid.
1. P→Q|=P→(R→P)
2. P→Q,Q→R|=P∨¬R



Can someone please check whether my answer is correct for question 1?:

Posted Image

Posted Image

Btw, I don't have a clue what information the truth table gives me, but I did it anyway cos I'm asked to.

Edit: Apologies, I made a mistake. In the image, where I wrote the statement letters, I should have put:

P = T
Q = T (not false)
R = T

This post has been edited by TechSyndrome: 08 August 2012 - 07:23 PM


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#2 e_i_pi  Icon User is offline

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Re: Check validity of argument - Propositional Logic

Posted 08 August 2012 - 09:00 PM

If I'm not too rusty on this sort of thing, it looks like you're close, but you've put TRUE for P0Q1R0 where it should be FALSE. This is what I got:

P Q R P->Q R->P P->(R->P)
0 0 0  1    1    0
0 0 1  1    0    1
0 1 0  1    1    0
0 1 1  1    0    1
1 0 0  0    1    1
1 0 1  0    1    1
1 1 0  1    1    1
1 1 1  1    1    1


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#3 blackcompe  Icon User is offline

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Re: Check validity of argument - Propositional Logic

Posted 09 August 2012 - 03:53 AM

Assuming the table is correct, the first argument isn't valid, since there exists a case where the premise is true and the conclusion is false. As stated, you've misunderstood logical consequence, so you need to fix that first. The only time that rule is false is when the antecedent is true, and the consequent is false.
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