19 votes 19 votes Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$ Mathematical Logic gate1989 normal mathematical-logic propositional-logic multiple-selects + – makhdoom ghaya asked Nov 27, 2016 • retagged Apr 16, 2021 by Lakshman Bhaiya makhdoom ghaya 3.8k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Lokesh . commented Nov 27, 2016 reply Follow Share A,B and C are equivalent 2 votes 2 votes Rajsukh Mohanty commented Sep 20, 2023 reply Follow Share Note that, relating to conditional and biconditional statements, and their converse, inverse, or contrapositive: only a conditional and its contrapositive are equivalent (p → q ≡ ¬q → ¬p), and only a biconditional and its inverse are equivalent (p ↔ q ≡ ¬p ↔ ¬q). 0 votes 0 votes Please log in or register to add a comment.
Best answer 24 votes 24 votes $P→Q \equiv \neg P\vee Q$ $¬Q→¬P\equiv Q\vee \neg P$ $¬P\vee Q \equiv \neg P \vee Q$ So, $A,B,C$ are equivalent . focus _GATE answered Nov 27, 2016 • selected Nov 27, 2016 by focus _GATE focus _GATE comment Share Follow See all 0 reply Please log in or register to add a comment.
8 votes 8 votes $P\rightarrow Q \equiv \neg P \vee Q$ $\neg Q\rightarrow \neg P\equiv \neg(\neg Q)\vee \neg P \equiv \neg P \vee Q$ $\neg P\vee Q$ $\neg Q \rightarrow P\equiv \neg (\neg Q) \vee P \equiv P \vee Q$ So, $A,B$ and $C$ are equivalent. Lakshman Bhaiya answered May 1, 2017 • edited Oct 8, 2019 by Lakshman Bhaiya Lakshman Bhaiya comment Share Follow See all 0 reply Please log in or register to add a comment.
7 votes 7 votes A,B,C are equavelent i.e. $P\rightarrow Q \equiv \sim P \vee Q$ A and C are equal because if $\rightarrow$ is true then Contradiction always true. Prashant. answered Nov 27, 2016 • edited Nov 27, 2016 by Prashant. Prashant. comment Share Follow See all 6 Comments See all 6 6 Comments reply Lokesh . commented Nov 27, 2016 reply Follow Share D is not equivalent 0 votes 0 votes Prashant. commented Nov 27, 2016 reply Follow Share Already done 1 votes 1 votes Arjun commented Nov 27, 2016 reply Follow Share How D? 0 votes 0 votes Prashant. commented Nov 27, 2016 reply Follow Share i was taken as $\sim$(Q $\rightarrow$ P) 0 votes 0 votes Arjun commented Nov 27, 2016 reply Follow Share That is also not true. 0 votes 0 votes Prashant. commented Nov 27, 2016 reply Follow Share I know that sir Or wil changes to And. thats why changed that. 3 votes 3 votes Please log in or register to add a comment.
2 votes 2 votes Let P and Q be statements. 1. (P→Q)⇔(¬P V Q), 2. (P→Q)⇔(¬Q→¬P), that is, the implication P→Q is logically equivalent to the contrapositive ¬Q→¬P. Hence 1 2 and 3 are equivalent. vupadhayayx86 answered Oct 8, 2019 vupadhayayx86 comment Share Follow See all 0 reply Please log in or register to add a comment.