Stuck on biconditional transposition: Philosophy Forums

Stuck on biconditional transposition

jordan716
Initiate

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Joined: Oct 29, 2009

Total Topics: 1
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Posted 10/29/09 - 07:29 PM: Subject: Stuck on biconditional transposition	#1
To anyone that can help: I am currently trying to solve the biconditional transposition proof: P <-> Q -\|\|- ~Q <-> ~P I know vaguely where to begin... I know I need RAA and I tried assuming the denial of the conclusion on both sides of the turnstile but I am a bit fuzzy after that. Any help would be appreciated! Thanks a lot.

frank2010
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Joined: Oct 11, 2009

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Total Posts: 32

Posted 10/29/09 - 11:50 PM:	#2
(1) P <-> Q, ASSUMPTION (2) P -> Q, 1->E (3) ~Q -> ~P, 2 TRANSPOSITION (4) Q -> P, 1 ->E (5) ~P -> ~Q, 4 TRANSPOSITION (6) (~Q -> ~P) & (~P -> ~Q), 3,5 &I (7) ~Q <-> ~P, 6 <->I Q.E.D.

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