Logic: Negating if then statement


by mohabitar
Tags: logic, negating, statement
mohabitar
mohabitar is offline
#1
Sep7-10, 11:32 PM
P: 140
I'm trying to negate this statement and wanna make sure I'm doing it right.
(p[tex]\vee[/tex]q) ---> (p [tex]\wedge[/tex] q)

So I dont negate both sides do I or else that would just make them equal out again? So I just negated the left side, so [tex]\neg[/tex](p[tex]\vee[/tex]q) is equivalent to [tex]\neg[/tex]p[tex]\wedge[/tex][tex]\neg[/tex]q

So thats the answer I got:
[tex]\neg[/tex]p[tex]\wedge[/tex][tex]\neg[/tex]q ---> (p [tex]\wedge[/tex] q)
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JonF
JonF is offline
#2
Sep8-10, 12:05 AM
P: 617
p=>q = ~p or q

Using de morgans law : ~(p=>q) = ~(~p or q) = p and ~q

So ~(p or q implies p and q) = p or q and ~(q and p) -> p or q and ~q or ~p -> p xor q
mohabitar
mohabitar is offline
#3
Sep8-10, 01:24 AM
P: 140
Sorry Im new to all this and what you have up there is very confusing. I cant really tell whats going on and what the final answer is. Anyway you can use the actual math symbols and break the steps into separate lines? I'd really appreciate it :)

vela
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#4
Sep8-10, 05:30 AM
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P: 11,534

Logic: Negating if then statement


JonF's already done too much work for you. It's against the forum rules to simply do the problems for you. You're supposed to work them out yourself.

Use the fact that you can write p→q as (~p)∨q. The latter form is easier to see how to negate.
mohabitar
mohabitar is offline
#5
Sep8-10, 01:24 PM
P: 140
Ya you're right sorry..I was just having a hard time understanding the symbols he was using but I think I got it now..so the final answer I got was:

(p v q) ^ (~p v ~q)

Is this what you had?
vela
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#6
Sep8-10, 01:52 PM
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P: 11,534
That's correct. You can simplify it a bit if you want.


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