The given truth table relates Y to A and B.
`{:("A","B","Y"),(0,0,1),(0,1,0),(1,0,0),(1,1,0):}`
Then, Y is given by

Options

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

Answer

To solve the problem, we need to analyze the given truth table and determine the logical expression for Y in terms of A and B.

### Step-by-Step Solution:

1. **Understand the Truth Table**:
The truth table provided is:
```
A | B | Y
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 0
```
From this table, we can see the output Y is 1 only when both A and B are 0.

2. **Identify Conditions for Y**:
We need to find a logical expression that results in Y being 1 only when A = 0 and B = 0.

3. **Use Logical Operators**:
The output Y can be expressed using logical operations. The condition where Y = 1 corresponds to the situation where both A and B are 0. This can be expressed as:
- Y = NOT(A OR B) or Y = (A + B)'

4. **Apply De Morgan's Theorem**:
According to De Morgan's theorem, the negation of an OR operation can be expressed as an AND operation with negated inputs:
- Y = (A + B)' = A'B'

5. **Final Expression**:
Therefore, the logical expression for Y in terms of A and B is:
- Y = A'B'

### Conclusion:
The expression for Y based on the truth table is:
\[ Y = \overline{A + B} \]
or equivalently,
\[ Y = A'B' \]