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 Post subject: Logic: TautologyPosted: Tue, 18 Jan 2011 15:19:23 UTC
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Joined: Fri, 12 Nov 2010 07:00:12 UTC
Posts: 48
Which of the following is NOT a tautology?

(A)

(B)

(C)

(D)

(E)

Source: Cracking the Mathematics GRE, Princeton Review..

I would think the answer is option C AND E?

C is wrong since
A: True
B: False
C: False
would produce a true value for the "left-hand side" while producing a false value for the 'right hand side'

E is also wrong since
A: True
B: False
C: False
would produce the necessary counterexample.

Is there anything wrong with my above reasoning?

I am very confused by the book's answer: Finally, choice (E) is the Distributive Property for sentential logic (clearly wrong??), so the statement is always true regardless of the values of sentences A, B, and C.

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 Post subject: Re: Logic: TautologyPosted: Tue, 18 Jan 2011 16:59:53 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, yoyobarn!

I agree with you.

. is not the Distributive Property.

Probably a typo . . . a spectacular one!

Either the left side is: .

. .or the right side is: .

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 Post subject: Posted: Wed, 19 Jan 2011 06:06:56 UTC
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Joined: Fri, 12 Nov 2010 07:00:12 UTC
Posts: 48
Thanks a lot, Soroban!

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