Question

As per Boolean algebra, (A + B)(A + C) = _______.

• A. A + BC
• B. AB + AC
• C. A
• D. B

Hint:

Use Boolean identities like $A + AB = A$ and $A + AC = A$ to simplify expressions.

Answer 1

The Correct Option is A

Using Boolean algebra identity: \[ (A + B)(A + C) = A + BC \] Proof: Expand using distributive law: \[ (A + B)(A + C) = AA + AC + AB + BC = A + AC + AB + BC \] But in Boolean algebra: $AA = A$ $A + AC = A$ $A + AB = A$ So, \[ A + AC + AB + BC = A + BC \] Therefore, (A + B)(A + C) = A + BC