Question

Propositional Logic

Is the following formula in Conjunctive Normal Form? Why? Why not?

(¬A) n (A u B) n ¬(A u B)

where A and B are propositional variables.

Answer 1

Given (¬A)   (A B)   ¬(A B)

The above Formula is Not in Conjunctive Normal Form

Because  in Conjunctive Normal Form the the Formula must have Conjunction of clauses Here in above Formula Negation must be applied inside the braces it should be Conjunction of clauses

In order to convert the above formula in Conjunctive Normal Form Negation must be applied inside the braces it should be Conjunction of clauses.

(¬A)   (A B)   ¬(A B)

(¬A)   (A B)   ¬(A B)

(¬A)   (A B)   (¬A ¬B)

(¬A)   (A B)   (¬A) (¬B) {By De Morgan's law ¬ (P Q) = ¬P ¬Q }

(¬A)   (A B)   (¬A) (¬B)

Which is Required Conjunctive Normal Form for given Formula