Question

Given the conditional statement ~p → q, which statement is logically equivalent?

A. p → ~q
B. ~p → ~q
C. ~q → ~p
D. ~q → p

Answer 1

Answer: option D. ~q → p


Step-by-step 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.