conjunctive-normal-form

How to convert it into CNF(Conjunctive normal form )

i faced a expression which is below

A ∨ (B ∧ C) ∨ (D ∧ E ∧ ￢ (A ∨ B))

how to Convert into CNF(Conjunctive normal form)?

Solution

  • Assuming you want an equivalent formula you have to use transformations that preserves logical equivalence.

    Here is a potential first step;

    A ∨ (B ∧ C) ∨ (D ∧ E ∧ ￢(A ∨ B))
((A ∨ B) ∧ (A ∨ C)) ∨ (D ∧ E ∧ ￢A ∧ ￢B)

    Taking distribution laws for A ∨ (B ∧ C) and applying DeMorgan to ￢(A ∨ B)