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Logic proof

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Logic proof
Christim
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Joined: Feb 28, 2009

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Posted 11/07/09 - 03:46 PM:
Subject: Logic proof
quote post
#1
Prove or disprove that the following rule of inference is sound:
Hint: You can use a truth table, but a careful logical
argument will also do it.

(p \/ q \/ r)
(~p \/ s)
---------------
(q \/ r \/ s)
frank2010
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Posted 11/08/09 - 01:00 AM:
quote post
#2
Hi, here's my proof:

1) p v (q v r) Assumption
2) ~p v s Assumption
3) ~p -> (q v r) 1 Material Implication
4) p -> s 2 Material Implication
5) ~(q v r) -> p 3 Trasp
6) ~(q v r) -> s 4,5 Syll
7) (q v r) v s 6 Material Implication

Q.E.D.
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