What is the value of A.C + A.B.C where A, B and C are inputs?

Options

A. A.C
B. A.B
C. A
D. B

Answer

To solve the expression A.C + A.B.C, we can simplify it using Boolean algebra.

### Step-by-Step Solution:

1. **Identify the Expression**:
We start with the expression A.C + A.B.C.

2. **Factor Out Common Terms**:
Notice that A is a common factor in both terms of the expression. We can factor A out:
\[ A.C + A.B.C = A(C + B.C) \]

3. **Simplify the Expression Inside the Parentheses**:
Now we need to simplify the expression inside the parentheses, C + B.C. According to Boolean algebra, we can use the Absorption Law which states that X + X.Y = X + Y. Here, we can apply it as follows:
\[ C + B.C = C(1 + B) = C \]
(since 1 + B = 1 in Boolean algebra).

4. **Substitute Back**:
Now substitute back into the factored expression:
\[ A(C + B.C) = A.C \]

5. **Final Expression**:
Therefore, the simplified expression is:
\[ A.C \]

### Conclusion:
The value of the expression A.C + A.B.C simplifies to A.C.