# The following question is a philosophic question.--(Truth Table) Suppose p and q are True (Arguments), r is a False (Argument), what is the truth value of the following statement? (True, False, or...

The following question is a philosophic question.--(Truth Table)

Suppose p and q are True (Arguments), r is a False (Argument), what is the truth value of the following statement? (True, False, or Unknown)

(p↔q)→r

The Original Question: [(s·r)↔(q v ~p)]→~(p·b)    (s and b are unknown)

[(~a v b) ↔~(~b→~a)]→r         (a, and b are unknown)

Guesses for the questions: unknown,     false    (but I'm not sure about both of it, so please give me some explanations as far as possible, thank you~^^)

ishpiro | Certified Educator

We can use the following truth table to determine the truth value of the given statement:

p    q      p -> q       q->p

T     T       T               T

T     F        F               T

F     T       T               F

F      F       T               T

If both p and q are true, then both the implication p -> q is true and its converse q ->p is true. Then, the statement in parenthesis, p <-> q, which means p -> q AND q -> p,  is true.

Since r is false, the implication in question, (p <-> q) -> r, is also false. (An implication is false when the original statement is true and the statement that follows is false.)

This means the truth value of the statement (p <-> q) -> r is FALSE.