3 votes 3 votes $P$ and $Q$ are two prepositions. Which of the following logical expressions are equivalent? $\neg Q\rightarrow \neg P$ $\neg P \vee Q$ $P \rightarrow Q$ $\neg P \wedge Q$ I, IV I, II, III II, IV I, II, III, IV Mathematical Logic go2025-dm-1 proportional-logic-order easy + – gatecse asked Jun 21, 2020 • recategorized Jun 21, 2020 by soujanyareddy13 gatecse 108 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes I and III are contrapositive statements and so are equivalent. I and II are also equivalent. IV is not equal to any of other three. Correct Answer is B gatecse answered Jun 21, 2020 gatecse comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes $\neg Q\rightarrow \neg P \equiv \neg(\neg Q) \vee \neg P \equiv Q \vee \neg P \equiv \neg P \vee Q = P \rightarrow Q$ $\neg P \vee Q$ $P \rightarrow Q$ $\neg P \wedge Q$ First three are the same. So, the correct answer is $(B).$ Lakshman Bhaiya answered Jul 23, 2020 Lakshman Bhaiya comment Share Follow See all 0 reply Please log in or register to add a comment.