29 votes 29 votes The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only Mathematical Logic gatecse-2017-set1 mathematical-logic propositional-logic easy + – khushtak asked Feb 14, 2017 retagged Jun 25, 2017 by Silpa khushtak 8.9k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 32 votes 32 votes $(\neg P\to \neg Q)$ can also be written as $(P \vee \neg Q),$ so statement $3$ is correct. Now taking the contrapositive of $(\neg P\to \neg Q)$, we get $(Q\to P)$ hence statement $2$ is correct. So, the answer is OPTION (D). sriv_shubham answered Feb 14, 2017 edited Jun 19, 2021 by Lakshman Bhaiya sriv_shubham comment Share Follow See all 2 Comments See all 2 2 Comments reply Aboveallplayer commented Feb 14, 2017 reply Follow Share i also think the same... 0 votes 0 votes Arjun commented Jun 7, 2018 reply Follow Share Ref: 6 votes 6 votes Please log in or register to add a comment.
11 votes 11 votes Given statement : ~p $\Rightarrow$ ~q = ~(~p) $\vee$ ~q = p $\vee$ ~q = ~q $\vee$ p = q $\Rightarrow$ p $\therefore$ D should be answer. Kantikumar answered Feb 14, 2017 Kantikumar comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes Option D. $(\sim p) \Rightarrow (\sim q)$ $\sim (\sim p) \vee (\sim q)$ $p \vee (\sim q)$ $ (\sim q) \vee p$ ----------------> III is True $q \Rightarrow p$ -----------------> II is True Uzumaki Naruto answered Feb 14, 2017 Uzumaki Naruto comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes we know that p→ q is equivalent to ~p v q similarly ~p→~q will be equivalent to p v ~q (III) and implication is equivalent to contrapositive , ~p→~q will be equivalent to q→ p (II) answer: Both II & III ,OPTION D Smriti012 answered Feb 14, 2017 Smriti012 comment Share Follow See all 0 reply Please log in or register to add a comment.