Given the conditional statement: p → ~q Choose the logically equivalent statement. A. p → q B. ~p → q C. q → p D. q → ~p
Accepted Solution
A:
Answer: The correct option is(D) q → ~p.Step-by-step explanation: We are given to select the statement that is logically equivalent to the conditional statement p → ~q.We know thattwo conditional statements are said to be logically equivalent if the truth tables of both the statements are same. That is, they have same truth values under similar conditions.The truth table is given byp q ~p ~q p → ~q p → q ~p → q q → p q → ~pT T F F F T T T FT F F T T F T T TF T T F T T T F TF F T T T T F T TSo, the truth values of p → ~q is same as the truth values of q → ~p. They must be logically equivalent.Thus, option (D) is CORRECT.