Answer: option D. ~q → p
Explanation:
1) About notation: ~p means not p and ~q means not q.
The correct notation is with the symbol ~ above the letter, but here the editor does not permit to do that.
2) ~p → q is the conditional if not p then q.
That conditional states that not p (~p) is a sufficient condition to state the true of q.
p is called the antecedent and q is called the consequent.
So, the antecedent implies the consequent.
But, it also means that the negation of the consequent, q, is sufficient to state the negation of the antecedent, not p (double negation of p). That is symbolically represented by:
~q → ~ (~p) ≡ ~ q → p, which is the option D.
