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