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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 True solution Comment 4 of 4 |
Suppose a statement says, "This statement is true if and only if P is true." If it is true, then it is true if and only if P is true. Since the statement is true, P is true. If it is false, then it is not true if and only if P is true. Since the statement is not true, P is true. Therefore, P has to be true.

By E, we know that B is false. By D, we know that either A, B, or both A and B are true. Since B is false, A is true. By F, we know that C and E are not both true. Since G is true, exactly one of D, E, and F is true. Therefore, we have these possibilities.

ABCDEFG
TFTTFFT
TFTFFTT
TFFTFFT
TFFFTFT
TFFFFTT


  Posted by Math Man on 2014-04-23 18:08:09
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