Formel in Dnf umformen. Term: (A v -B) ∧ -(-A v (A ∧ -B))

Question

Hey Leute,

ich müsste diesen Term in die Disjunktive Normalenform bringen. Leider komm ich nicht auf diesen würde mich über Hilfe freuen

(A v -B) ∧ -(-A v (A ∧ -B))

Answer 1

Hi! :-)

(A v -B) ∧ -(-A v (A ∧ -B)) =
(A v -B) ∧ -((-A v A) ∧ (-A v -B)) =
(A v -B) ∧ -(-A v -B) =
(A v -B) ∧ (A ∧ B) =
(A v (A ∧ B)) v (-B ∧ (A ∧ B)) =
(A v A) ∧ (A ∧ B) v ((-B ∧ A) ∧ (-B ∧ B)) =
(1 ∧ (A ∧ B)) v ((-B ∧ A) ∧ 0) =
(A ∧ B) v 0 =
A ∧ B