if p implies q is true then the truth value of which of the following cannot be determined

Question

a) ~p\/q        b) ~q=>~p

c) ~p=>~q    d) ~(p/\~q)

can someone provide the solution?

Answer 1

We have p -> q as a true proposition.

That means for p as true and q as false we can't have the truth value as True. Because T -> F is False. 

Now since we have p = True and q = False as a test condition to check all the options we can use proof by examples to evaluate the final answer.

Option a: not p or q : not (True) or False = False or False = False. 

Option b: not q -> not p : not(False) -> not(True) = True-> False = False

Option c: not p -> not q : not(True) -> not(False) = False-> True = True (This is the wrong option)

Option d: not (p and not q) : not(True and not(False)) = not(True and True) = not(True) = False

So out of the given options only option c cannot be determined.