Re: Truth Tables!
- From: Jim Spriggs <jim.sprigs@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 28 May 2005 00:22:02 +0000 (UTC)
1st Semester Logic Student wrote:
> Problem goes like this:
> 3. Say whether each of the following are truth-functionally true,
> truth-functionally false, or truth-functionally indeterminate by
> constructing a truth-table. (You may use a shortcut method if you
>
> a) (E tripplebar H) Horseshoe (-E horseshoe -H)
(E <-> H) -> (-E -> -H)
0 1 0 1 10 1 10
0 0 1 1 10 0 01
1 0 0 1 01 1 10
1 1 1 1 01 1 01
"Truth-functionally true", or "tautology" to use the usual term.
> b) ([C horseshoe D) & (D horseshoe E)] & C) & -E
((C -> D) & (D -> E)) & C) & -E
0 1 0 1 0 1 0 0 0 0 10
0 1 0 1 0 1 1 0 0 0 01
0 1 1 0 1 0 0 0 0 0 10
0 1 1 1 1 1 1 0 0 0 01
1 0 0 0 0 1 0 0 1 0 10
1 0 0 0 0 1 1 0 1 0 01
1 1 1 0 1 0 0 0 1 0 10
1 1 1 1 1 1 1 1 1 0 01
"Truth-functionally false", or "contradictory" to use the usual term.
> c) [(CvD) tripplebar C] horseshoe -C
((C v D) <-> C) -> -C
0 0 0 1 0 1 10
0 1 1 0 0 1 10
1 1 0 1 1 0 01
1 1 1 1 1 0 01
"Truth-functionally indeterminate", or "contingent" to use the usual
term.
> d) (B horseshoe H) & (B horseshoe -H)
(B -> H) & (B -> -H)
0 1 0 0 0 1 10
0 1 1 0 0 1 01
1 0 0 0 1 1 10
1 1 1 1 1 0 01
"Truth-functionally indeterminate", or "contingent" to use the usual
term.
Still no evidence that you've tried these for yourself.
.
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