In the Boolean algebra : `A + B =`

Options

A. `overline(A)+overline(B)`
B. `A.B`
C. `overline(overline(A))+overline(overline(B))`
D. `overline(overline(A))+overline(B)`

Explanation

To solve the question "In the Boolean algebra: A + B =", we will analyze the expression using Boolean algebra rules.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The expression A + B in Boolean algebra represents the logical OR operation. This means that the output is true (1) if either A is true (1), B is true (1), or both are true (1).

2. **Evaluating Each Option**:
We will evaluate four options to see which one is equivalent to A + B.

- **Option Y1: A + B**:
This is the original expression itself, so it is equal to A + B.

- **Option Y2: A' + B'** (where ' denotes NOT):
According to De Morgan's theorem, A' + B' is equivalent to (A * B)' (the complement of A AND B). This is not equal to A + B. Therefore, Y2 is not equal to Y.

- **Option Y3: (A')' + (B')'**:
Applying the double negation law, we find that (A')' = A and (B')' = B. Thus, this simplifies to A + B, which is equal to Y.

- **Option Y4: (A')' + B'**:
Here, (A')' = A, so this simplifies to A + B', which is not equal to A + B. Therefore, Y4 is not equal to Y.

3. **Conclusion**:
After evaluating all options, we find that only Y1 and Y3 are equivalent to A + B. Therefore, the correct answer is Y3.

### Final Answer:
A + B = Y3 (where Y3 = (A')' + (B')')