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Veracity Verification III (Posted on 2014-04-23) Difficulty: 3 of 5
The following statements are about Mr. Buford’s children:

A. Tracy is blond.
B. Joyce is over six feet tall.
C. Sabrina is in her 27th year.
D. This statement is true if A, or B, or both A and B are true; otherwise it is false.
E. This statement is true if B is false and vice versa.
F. This statement is false if and only if both C and E are true.
G. Just one of statements D, E, and F is true.

If I tell you that G is true, determine which of the statements A through F are true and which are false.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Meta-solution (spoiler) | Comment 1 of 4
Well, I am going to solve what I think is the intended problem, namely,

D. A, or B, or both A and B are true
E. B is false 
F. C and E are not both true. 
G. Just one of statements D, E, and F is true. 

Then a truth table is as follows

A B C D E F G
- - - - - - -
T T T T F T F
T T F T F T F
T F T T T F F
T F F T T T F
F T T T F T F
F F T F T F T <-- Solution
F F F F T T F

There is only one case where G is true, namely A and B False and C true

My problem with the original question is that D and E and F were meta-statements, namely statements about themselves.  I don't see any way to solve this if 2 of the meta-statements are false, since meta-statements don't really give any indication about the truth values of A or B or C.  In effect, I am taking all three meta-statements as true, and basing my solution on the truth value of the underlying statement.

  Posted by Steve Herman on 2014-04-23 13:43:53
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