Puzzle Logic
Posted on Wednesday, July 29th, 2009 at 10:52 pmPuzzle Logic
Can someone help me solve this logic puzzle?
A v ~A
I have to prove using symbolic logic that this theorem is credible.
Must be solved in the form of a proof.
I have to show it using only the 11 symbolic logic rules(no changing v to ^ and stuff like that).
Thank you!
This is a logical truth. It is called the law of the excluded middle. Here is the proof.
(1) -(A or -A) [assume for RAA]
(2) A [assume for RAA]
(3) A or -A [2, "or introduction"]
(4) (A or -A) & -(A or -A) [1, 3, "& introduction"]
(5) -A [2,4, RAA]
(6) A or -A [5, "or introduction"]
(7) (A or -A) & -(A or -A) [1,6, "& introduction"]
(8) – - (A or -A) [1,7, RAA]
(9) A or -A [8, "double negation"]
This proof is completed at line 9 with dependence on no assumptions, making it a logical truth/theorem.
Everyone has different names for the rules, but they are generally similar sounding, so you should get the point.
Hope this helps.
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