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 Post subject: Simplifying logical statements / CircutsPosted: Mon, 21 Mar 2011 20:53:57 UTC

Joined: Wed, 9 Mar 2011 22:13:06 UTC
Posts: 6
Could someone please verify that my thinking is correct in both cases? Thank you!
1)~q => (~p => q)

~(~q) v (~p => q)
q v (~p=>q)
q v (~(~p) v q)
q v (p v q)
(q v q) v p
q v p

2) the same example ~q => (~p => q)
~(~q) v (~p => q)
q v (~p=>q)
(q v ~p) => (q v q)
~ (q v ~p) v q
(~q ^ p) v q
(~q v q) ^ (p v q)
T ^ (p v q)
p v q

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 Post subject: Posted: Mon, 21 Mar 2011 21:21:05 UTC
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9632
Here's the WolframAlpha calculation.
Under minimal forms, you can see that p v q is one of the simplifications.

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 Post subject: Posted: Mon, 21 Mar 2011 22:26:43 UTC

Joined: Wed, 9 Mar 2011 22:13:06 UTC
Posts: 6
Thank you for the link. However, I would like to be sure that I am correctly applying the equivalences in all the steps. In other words if I am getting this result the right way.

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 Post subject: Posted: Mon, 21 Mar 2011 23:00:02 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
magwoj wrote:
Thank you for the link. However, I would like to be sure that I am correctly applying the equivalences in all the steps. In other words if I am getting this result the right way.

Yes.

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 Post subject: Posted: Mon, 21 Mar 2011 23:03:30 UTC

Joined: Wed, 9 Mar 2011 22:13:06 UTC
Posts: 6
Thank you!

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