Question

If p → q is true, then ~ q → ~ p is __________ false.
always
sometimes
never

Answer 1

Never I know its never

Answer 2

If p → q is true, then ~ q → ~ p is never false.

Explanation:

If p → q is true, then we need to check whether the statement ~ q → ~ p is true or false.

Truth table:

p q ~ p ~ q p → q ~ q → ~ p

T T F F T T

T F F T F F

F T T F T T

F F T T T T

From the above table it is clear that p → q is true, then ~ q → ~ p is always true.

If p → q is true, then ~ q → ~ p is never false.