# Need help on mathematical logic

• Sep 4th 2013, 09:39 PM
joseph1125
Need help on mathematical logic
Which of the following propositional forms are tautologies.

(p implies (q implies r)) implies ((p and not q) or r)

(p and not q) or (q and not r) or (r and not p)

I need help in both questions, btw, simplify only, no truth table

Thanks!
• Sep 5th 2013, 07:19 AM
emakarov
Re: Need help on mathematical logic
Can you determine whether they are tautologies using other means? How do you prove that something is not a tautology using simplifications?
• Sep 5th 2013, 10:52 AM
Hartlw
Re: Need help on mathematical logic
Quote:

Originally Posted by joseph1125
Which of the following propositional forms are tautologies.

(p implies (q implies r)) implies ((p and not q) or r)

(p and not q) or (q and not r) or (r and not p)

I need help in both questions, btw, simplify only, no truth table

Thanks!

Assume Definition of tautology: Statement that is always true.

Write first one as A->B and let p=q=r=F
Then A is F and B is F so A->B is False. Not a tautology.

Write second one as AorBorC and let p=q=r=F. Then A,B and C are false so AorBorC is false. Not a tautology.