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Topic: Tautology Proof Question
Replies: 1   Last Post: Mar 19, 2012 5:51 AM

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Angela Richardson

Posts: 42
From: UK
Registered: 6/22/11
Re: Tautology Proof Question
Posted: Mar 19, 2012 5:51 AM
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(p -> r) is equivalent to (¬p v r)    i.e p implies r means that r is true or p is not true.
(p v q) ^ (¬p v r) ^ (¬q v r)  and (p ^ ¬p) v (r ^ q) ^ (¬q v r)  both mean that  p or q is true, and r is true or p is false, and r is true or q is false.  
 
(p ^ ¬p) is false hence (r ^ q) ^ (¬q v r) is true, and r and q being true implies r is true. 

  

________________________________
From: Ashraf Samhouri <discussions@mathforum.org>
To: discretemath@mathforum.org
Sent: Monday, 19 March 2012, 8:51
Subject: Tautology Proof Question

Hello guys,

While studying, I've passed through this proof (in the class notes):

Example:
Proof that:
( (p v q) ^ (p -> r) ^ (q -> r) ) -> r
is a tautology?

The solution is:
( (p v q) ^ (¬p v r) ^ (¬q v r) ) -> r
( (p ^ ¬p) v (r ^ q) ^ (¬q v r) ) -> r
(F v (q ^ ¬q) v r) -> r
r -> r
¬r v r
.: T

Actually I can't understand the steps, am not sure if the notes are
well-written here, but I'll appreciate any help in explaining the
proof.

Regards,
ASH



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