What will be the input of A and B for the Boolean expression
`overline((A+B)).overline((A+B))=1`

Options

A. 0
B. 0,1
C. 1,0
D. 1,1

Explanation

To solve the Boolean expression `overline((A+B)).overline((A+B))=1`, we will analyze the expression step by step.

### Step 1: Understand the Expression
The expression can be simplified as follows:
- The expression `overline((A+B))` means the NOT operation on the sum (OR operation) of A and B.
- The entire expression is the AND of two identical terms: `overline((A+B)) AND overline((A+B))`.

### Step 2: Simplify the Expression
Since `X AND X = X`, we can simplify the expression:
- `overline((A+B)).overline((A+B)) = overline((A+B))`.

Thus, the equation we need to solve is:
- `overline((A+B)) = 1`.

### Step 3: Solve for A and B
The expression `overline((A+B)) = 1` implies that:
- `A + B = 0` (because the NOT of 0 is 1).

### Step 4: Analyze the Condition
For `A + B = 0`, both A and B must be 0:
- If A = 0 and B = 0, then `0 + 0 = 0`.

### Step 5: Conclusion
The only inputs for A and B that satisfy the original expression are:
- A = 0
- B = 0

### Final Answer
Thus, the input values for A and B are:
- A = 0, B = 0.

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