The Purplemath Forums

by **salvarez83** on Sun Oct 03, 2010 2:09 pm

Can someone show me how to simplify the following statement using laws. Such as communicative, distributive, de morgans law, etc?

I need to show:

~(p \/ ~q) \/ (~p /\ ~q)

Equals:

~p

Thanks.

**Sponsor**

by **Martingale** on Sat Oct 30, 2010 5:42 pm

salvarez83 wrote:Can someone show me how to simplify the following statement using laws. Such as communicative, distributive, de morgans law, etc?

I need to show:

~(p \/ ~q) \/ (~p /\ ~q)

Equals:

~p

Thanks.

$\sim (p \vee \sim q)\vee(\sim p \wedge \sim q)$

$=(\sim p \wedge q)\vee(\sim p \wedge \sim q)$

$=\sim p \wedge (q\vee \sim q)$

$=\sim p$

The Purplemath Forums

Simplify (Using Laws): show ~(p \/ ~q) \/ (~p /\ ~q) = ~p

Simplify (Using Laws): show ~(p \/ ~q) \/ (~p /\ ~q) = ~p

Re: Simplify (Using Laws): show ~(p \/ ~q) \/ (~p /\ ~q) = ~