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+2 votes

The resolvent of the set of clauses $(A \vee B, \sim A \vee D, C \vee \sim B)$ is 

  1. $A \vee​ B$
  2. $C \vee​ D$
  3. $A \vee​ C$
  4. $A \vee​ D$ 
in Mathematical Logic by Boss (30.8k points)
recategorized by | 1.1k views

3 Answers

+2 votes
Best answer

ans will be B) C   D


A & ~A will cancel out  and so will B and ~B 

hence ans  

by Boss (49.3k points)
selected by

Plz Tell the procedure of finding resolvent.


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 
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

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) $C \lor D$.

by Boss (41.3k points)
+1 vote


ans is B

by Active (1.9k points)

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