Re: truth-functionally equivalent
- From: Jim Spriggs <jim.sprigs@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 27 May 2005 20:07:33 +0000 (UTC)
1st Semester Logic Student wrote:
>
> Yet another one using truth tables. Any pointers, advice, answer,
> debate?
Two bits of advice: post in ascii only, to me only b) is readable.
And, you'll learn more if you do your own homework.
> 4. Say whether each of the following pairs of sentences are
> truth-functionally equivalent by constructing a truth-table. (You may
> use a shortcut method if you like).
> a) A â?? (Bâ??A); (C&-C) v (Aâ??A)
> b) C & (BvA); (C&B) v A
C & (B v A) (C & B) v A
0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 0 0 0 1 1 <
0 0 1 1 0 0 0 1 0 0
0 0 1 1 1 0 0 1 1 1 <
1 0 0 0 0 1 0 0 0 0
1 1 0 1 1 1 0 0 0 1 <
1 1 1 1 0 1 1 1 1 0
1 1 1 1 1 1 1 1 1 1
Since the rows marked < differ in truth value they are not equivalent.
> c) A â?? [B â?? (Aâ??B)]; B â?? [A â?? (B â?? A)]
> d) A â?¡ (-A â?¡ A); -(Aâ??-A)
>
> Thanks!
.
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