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How do I prove this statement is a tautology, without using truth tables?

makoten · 2011-11-02 17:40:30

Only the laws can be used, no truth tables allowed. Prove the statement: ((p V q) ^ (p -> r) ^ (q -> r)) -> r is a tautology. I am genuinely stuck, even though the laws are right in front of me I don't know where to start!

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02-11-2011 6:40pm

#1

makoten

Registered Users Posts: 138 ✭✭

Join Date: April 2010

Posts: 125

Only the laws can be used, no truth tables allowed.

Prove the statement:
((p V q) ^ (p -> r) ^ (q -> r)) -> r
is a tautology.

I am genuinely stuck, even though the laws are right in front of me I don't know where to start!

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#2 03-11-2011 12:43am
Fremen

Registered Users Posts: 2,481 ✭✭✭

Join Date: May 2006

Posts: 2356

Maybe you should post up what laws you're allowed to use. My strategy would be to eliminate the -> signs by re-writing them as ANDs and ORs. Then use the fact that (p OR not p) is always true.

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