Given the following truth table where A , B are inputs and Y the output :
`{:(A,B,Y),(0,0,1),(1,0,1),(0,1,1),(1,1,0):}`
The output Y is :

Options

A. `A bar(B)`
B. `bar(A) B`
C. AB
D. `bar(AB)`

Answer

To solve the problem, we need to analyze the given truth table and determine the logical expression that corresponds to the output Y based on the inputs A and B.

### Step-by-Step Solution:

1. **Understand the Truth Table**:
The truth table provided is:
```
A | B | Y
---------
0 | 0 | 1
1 | 0 | 1
0 | 1 | 1
1 | 1 | 0
```
Here, we have two inputs (A and B) and one output (Y).

2. **Identify the Conditions for Output Y**:
- From the truth table, we can see that Y is 1 when:
- A = 0 and B = 0
- A = 1 and B = 0
- A = 0 and B = 1
- Y is 0 only when A = 1 and B = 1.

3. **Determine the Logical Expression**:
- The output Y is 1 for all combinations of A and B except when both are 1. This indicates that Y is true when at least one of A or B is false.
- The logical expression that describes this condition is:
\[ Y = \overline{A \land B} \]
- This expression represents a NAND gate, which outputs 1 for all input combinations except when both inputs are 1.

4. **Final Expression**:
- Thus, the output Y can be expressed as:
\[ Y = \overline{A \land B} \]
- This means Y is the output of a NAND gate with inputs A and B.

### Conclusion:
The output Y is given by the expression \( Y = \overline{A \land B} \), which corresponds to the NAND operation.