Which term is redudent in the expression AB+A’C+BC?

Which term is redudent in the expression AB+A’C+BC? Correct Answer BC

The Correct Answer is BC

The simplification of the boolean expression:

AB+A’C+BC =  = AB + A’C + BC*1 {as A*1 = A}

= AB + A’C + BC(A + A’) {as Complement law: A + A’ = 1}

= AB + A’C + ABC + A’BC {as Absorption law: A(B + C) = AB + BC & AB = BA}

= AB + ABC + A’C + A’CB {as Commutative Law: A + B = B + A & AB = BA}

= AB*1 + ABC + A’C*1 + A’CB {as A*1 = A}

= AB(1 + C) + A’C(1 + B) {as AB + BC = A(B + C)}

= AB*1 + A’C*1 {as 1 + A = 1}

= AB + A’C {as A*1 = A}

Hence the redundant term in the given expression is BC

Additional InformationWe can directly evaluate this using Consensus theorem, i.e.

AB + A'C + BC = AB +A'C

Important Points