Simplifying Boolean Expression A + AB

We need to simplify the given Boolean expression:

$ A + AB $

Applying Boolean Algebra Rule

This expression can be simplified using the Absorption Law in Boolean algebra. The Absorption Law states that for any Boolean variables X and Y:

$ X + XY = X $

Step-by-Step Simplification

Let's apply this law to our expression $ A + AB $.

1. Identify $ X $ and $ Y $ in the expression $ A + AB $. Here, $ X = A $ and $ Y = B $.
2. Apply the Absorption Law formula $ X + XY = X $.
3. Substituting $ X = A $ and $ Y = B $ into the formula, we get: $ A + AB = A $.

Alternatively, we can factor out A:

$ A + AB = A(1 + B) $

Using the Identity Rule ($ 1 + B = 1 $):

$ A(1) = A $

Final Result

Both methods confirm that the simplified form of the Boolean expression $ A + AB $ is $ A $.

Options Review

Comparing this result with the given options:

• Option 1: B
• Option 2: A+1
• Option 3: AB
• Option 4: A (This matches our result)