In Boolean algebra, which of the following is not equal to zero :-

Options

A. `A.bar(A)`
B. A.0
C. `bar(A+bar(A))`
D. `bar(bar(A).0)`

Answer

To solve the question regarding which expression in Boolean algebra is not equal to zero, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Evaluate A . A' (A AND NOT A)**:
- According to Boolean algebra, A AND NOT A (A . A') is always equal to 0.
- If A = 1, then A' = 0, so A . A' = 1 . 0 = 0.
- If A = 0, then A' = 1, so A . A' = 0 . 1 = 0.
- Therefore, A . A' = 0.

2. **Evaluate A . 0 (A AND 0)**:
- A AND 0 is also always equal to 0.
- Regardless of the value of A (whether A = 1 or A = 0), A . 0 = 0.
- Therefore, A . 0 = 0.

3. **Evaluate A + A' (A OR NOT A)**:
- A OR NOT A (A + A') is always equal to 1.
- If A = 1, then A' = 0, so A + A' = 1 + 0 = 1.
- If A = 0, then A' = 1, so A + A' = 0 + 1 = 1.
- Therefore, A + A' = 1, which is not equal to 0.

4. **Evaluate (A + 0)' (NOT (A OR 0))**:
- A + 0 simplifies to A, so (A + 0)' = A'.
- A' is not necessarily equal to 0; it depends on the value of A.
- If A = 1, then A' = 0.
- If A = 0, then A' = 1.
- Therefore, A' can be either 0 or 1, so it is not guaranteed to be equal to 0.

5. **Conclusion**:
- From the evaluations, we find that:
- A . A' = 0
- A . 0 = 0
- A + A' = 1 (not equal to 0)
- (A + 0)' = A' (not guaranteed to be 0)
- Therefore, the expression that is **not equal to 0** is **A + A'**.

### Final Answer:
The expression that is not equal to zero is **A + A'**.