2 votes 2 votes The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is $A \vee B$ $C \vee D$ $A \vee C$ $A \vee D$ Mathematical Logic ugcnetcse-dec2014-paper3 mathematical-logic + – makhdoom ghaya asked Jul 30, 2016 • recategorized Jul 30, 2016 by LeenSharma makhdoom ghaya 4.6k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes ans will be B) $C \vee D$ $A \vee B,\ \sim A \vee D,\ C \vee \sim B$ $A$ and $\sim A$ will cancel out and so will $B$ and $\sim B$ hence ans Sanjay Sharma answered Jul 30, 2016 • edited May 7, 2021 by Shiva Sagar Rao Sanjay Sharma comment Share Follow See all 3 Comments See all 3 3 Comments reply Prashant. commented Jul 30, 2016 reply Follow Share Plz Tell the procedure of finding resolvent. 0 votes 0 votes LeenSharma commented Jul 30, 2016 reply Follow Share https://en.wikipedia.org/wiki/Resolution_%28logic%29 0 votes 0 votes Sanjay Sharma commented Jul 30, 2016 i edited by Tauhin Gangwar Jul 30, 2016 reply Follow Share Robinson in 1965 introduced the resolution principle, which can be directly applied to any set of clauses. The principal is "Given any two clauses A and B, if there is a literal P1 in A which has a complementary literal P2 in B, delete P1 & P2 from A and B and construct a disjunction of the remaining clauses. The clause so constructed is called resolvent of A and B." For example, consider the following clauses A: P V Q V R B: p' V Q V R C: Q' V R Clause A has the literal P which is complementary to `P in B. Hence both of them deleted and a resolvent (disjunction of A and B after the complementary clauses are removed) is generated. That resolvent has again a literal Q whose negation is available in C. Hence resolving those two, one has the final resolvent. A: P V Q V R (given in the problem) B: p' V Q V R (given in the problem) D: Q V R (resolvent of A and B) C: Q' V R (given in the problem) E: R (resolvent of C and D) 2 votes 2 votes Please log in or register to add a comment.
2 votes 2 votes Resolvent is the outcome of applying the resolution rule. $\frac{{A\lor B , \thicksim A \lor B, C \lor \thicksim D}}{C \lor D}$ Hence,Option(B) $C \lor D$. LeenSharma answered Jul 30, 2016 LeenSharma comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes ans is B Prasanjeet Ghosh answered Jun 16, 2018 Prasanjeet Ghosh comment Share Follow See all 0 reply Please log in or register to add a comment.