NIMCET 2017 — Computer PYQ
NIMCET | Computer | 2017Which term is redudent is the expression AB+A’C+BC?
Choose the correct answer:
- A.
BC
- B.
A’C
- C.
AB
- D.
AB + A'C
(Correct Answer)
AB + A'C
Explanation
The Correct Answer is AB + A'C
- 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}.
Explanation
The Correct Answer is AB + A'C
- 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}.