Question

Prove following using the Boolean algebraic theorems: a. A + A’B + AB’ = A + B​

Answer 1

Explanation:

A + B) * (A’ + C)

→ AA’ + AC + A’B + BC

→ 0 + AC + A’B + BC

→ AC + CB + A’B

By the consensus theorem:

xy + yz + x’z = xy + x’z

Let A = x, B = z, C = y

→ AC + CB + A’B = xy + yz + x’z

→ AC + A’B = xy + x’z

Therefore, (A + B) * (A’ + C) = AC + A’B