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.
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.
Meta-solution (spoiler)
