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)
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~^^)
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.