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**aperson** · 05-11-2007, 04:07 PM

Logic puzzle:

Axioms:
Ax 1: [A -> (B -> A)]
Ax 2: (A -> B) -> {[A -> (B -> C)] -> (A -> C)}
Ax 3: (~B -> ~A) -> (A -> B)

Prove:
~A -> (A -> B)
then prove
~~A -> A
then prove
(A -> B) -> (~B -> ~A)

where -> is the standard implication structure

05-11-2007, 04:07 PM	#85
aperson FFR Hall of Fame Join Date: Jul 2003 Location: Houston Posts: 3,431	Re: Logic Puzzles Logic puzzle: Axioms: Ax 1: [A -> (B -> A)] Ax 2: (A -> B) -> {[A -> (B -> C)] -> (A -> C)} Ax 3: (~B -> ~A) -> (A -> B) Prove: ~A -> (A -> B) then prove ~~A -> A then prove (A -> B) -> (~B -> ~A) where -> is the standard implication structure __________________