Math Is Fun Forum

Extreme112

Guest

Discrete Math Help

¬ (p ^ (q ∨ r) ^ ((p ^ q) > r)) Simplify >
¬ (p ^ (q ∨ r) ^ (¬ (p ^ q) ∨ r)) DE Morgan’s Law
¬p ∨ ¬ (q ∨ r) ∨ ¬ (¬ (p ^ q) ∨ r)    DE Morgan’s Law
¬p ∨ ¬q ^ ¬r ∨ (p ^ q) ^ ¬r

So I've reached this last step and I'm not sure how to simplify this further. The only thing I see is a Distributive Property of (p ^ q) ^ ¬r , but I'm not sure if this is allowed. Any help would be great.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Discrete Math Help

You cannot remove parentheses when you have something lik p AND (q OR r).

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Discrete Math Help

hi Extreme112

Welcome to the forum.

If your first line is correct (I'm doubtful about that > ) then you haven't used de Morgan correctly.

This is the analysis of what you have posted.

Please check what you have posted and confirm it is correct. 

Bob

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