In Boolean algebra `A + B = Y` implies that :

Options

A. output Y exists when both input A and B exist
B. output Y exists when either input A exists or input B exists or both inputs A and B exist
C. output Y exists when either input A exists or input B exists but not when both inputs A and B exist
D. output Y exists when both inputs A and B exists but not when either input A or B exists

Answer

To solve the question "In Boolean algebra `A + B = Y` implies that:", we need to analyze the expression and its implications in the context of Boolean algebra.

### Step-by-Step Solution:

1. **Understanding the Expression**:
- The expression `A + B = Y` in Boolean algebra means that Y is true if at least one of A or B is true.

2. **Interpreting the "+" Operator**:
- In Boolean algebra, the "+" operator represents the logical OR operation. Therefore, `A + B` implies that Y will be true if A is true, B is true, or both A and B are true.

3. **Identifying Conditions for Y**:
- For Y to be true (Y = 1), the following conditions must be satisfied:
- If A = 1 (true), then Y = 1.
- If B = 1 (true), then Y = 1.
- If both A and B = 1, then Y = 1.

4. **Conclusion**:
- Thus, we can conclude that the expression `A + B = Y` implies that Y exists when either A exists, or B exists, or both A and B exist.

5. **Selecting the Correct Option**:
- Based on the implications derived from the expression, the correct option would be the one that states "Y exists when either A exists or B exists or both".

### Final Answer:
The correct implication of `A + B = Y` is that Y exists when either A exists, or B exists, or both A and B exist.

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