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Math Forum » Discussions » Math Topics » discretemath

Topic: logical equivalence problem
Replies: 8   Last Post: Dec 8, 2008 8:42 PM

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mike1234

Posts: 3
Registered: 11/29/08
logical equivalence problem
Posted: Nov 29, 2008 12:41 AM
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Hello everyone, I've been asked to show with logical equivalence laws that...

~(p <--> q) is equivalent to (~q) <--> p)

I have tried working both sides of this one and keep getting stuck at certain points. By truth table, it is easy to see that they are equivalent.

This is how I've tried working the left side...

~(p <--> q)
~((p->q)^(q->p)) bicond. written as (if and if)
~((~p v q) ^ (~q v p)) if-then written as or stmnt
~(~p v q) v ~(~q v p) De Morgan's law
(p ^ ~q) v (q ^ ~p) De Morgan's law
~(p -> q) v ~(q -> p) negation of if stmnt

This is pretty much where I get stuck. Any suggestions would be greatly appreciated.


Message was edited by: mike1234

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