Correct Answer  Option 4 : ABC + ABC' + AB'C
Concept:
Important Axioms and De Morgan's laws of Boolean Algebra:
 Double inversion \(\overline{\overline A} = A\)
 A . A = A
 A . \(\overline A \) = 0
 A + 1 = 1
 A + A = A
 A + \(\overline A \) = 1
De Morgan's laws:
Law 1: \(\overline {{\bf{A}} + {\bf{B}}} = \overline{A}\;.\overline B\)
Law 2: \(\overline {{\bf{A}}\;.{\bf{B}}} = \overline A +\overline B\)
Calculation:
Let the given function be Y
Y = AB + AC
Now expanding by using the important properties of boolean algebra:
Y = AB(C + C̅) + AC(B + B̅)
Y = ABC + ABC̅ + ACB + ACB̅
As ABC + ACB = ABC
Y = ABC + ABC̅ + ACB̅
Y can also be written as:
Y = ABC + ABC' + AB'C
Hence option (4) is the correct answer.
Name

AND Form

OR Form

Identity law

1.A=A

0+A=A

Null Law

0.A=0

1+A=1

Idempotent Law

A.A=A

A+A=A

Inverse Law

AA’=0

A+A’=1

Commutative Law

AB=BA

A+B=B+A

Associative Law

(AB)C

(A+B)+C = A+(B+C)

Distributive Law

A+BC=(A+B)(A+C)

A(B+C)=AB+AC

Absorption Law

A(A+B)=A

A+AB=A

De Morgan’s Law

(AB)’=A’+B’

(A+B)’=A’B’
