Question

Simplify A'(A + B) + (B + AA)(A + B')

Answer 1

To simplify the expression A'(A + B) + (B + AA)(A + B'), apply the distributive property and negation rule. The simplified expression is A' × B.

Step-by-step explanation:

To simplify the expression A'(A + B) + (B + AA)(A + B'), we can start by applying the distributive property and negation rule. We get:

1. A'(A) + A'(B) (distributive property)
2. A' × A + A' × B (negation rule)

Next, we simplify the terms:

1. 0 + A' × B (A' × A = 0)
2. A' × B

Therefore, the simplified expression is A' × B.

Answer 2

The simplified expression for A'(A + B) + (B + AA)(A + B') is A'B + AB'.

Step-by-step explanation:

To simplify the given Boolean expression, apply the Boolean algebra rules. Start by distributing A' over the terms inside the first parentheses, which results in A'B + A'A. Since A'A is always 0 (identity law), the first part simplifies to A'B.

Now, focus on the second part of the expression (B + AA)(A + B'). Apply the absorption law (AA = A) to simplify to (B + A)(A + B'). Distribute the terms, and then use the idempotent law (A + A = A) to further simplify, resulting in AB' + A'B.

Combine the simplified expressions for both parts: A'B + AB'.