The truth table given below is for :-
`{:(A,B,Y),(0,0,1),(0,1,0),(1,0,0),(1,1,1):}`

Options

A. OR gate
B. AND gate
C. XNOR gate
D. XOR gate

Answer

To determine which logic gate the given truth table represents, we will analyze the truth table step by step and compare it with the Boolean expressions of different gates.

### Given Truth Table:
- A | B | Y
- 0 | 0 | 1
- 0 | 1 | 0
- 1 | 0 | 0
- 1 | 1 | 1

### Step 1: Identify the Logic Gates
We will consider the following logic gates:
1. OR Gate: \( Y = A + B \)
2. AND Gate: \( Y = A \cdot B \)
3. XNOR Gate: \( Y = A \cdot B + \overline{A} \cdot \overline{B} \)
4. XOR Gate: \( Y = \overline{A} \cdot B + A \cdot \overline{B} \)

### Step 2: Check Each Gate Against the Truth Table

#### Check OR Gate
- For \( A = 0, B = 0 \): \( Y = 0 + 0 = 0 \) (Expected: 1)
- **Conclusion**: OR gate does not satisfy the truth table.

#### Check AND Gate
- For \( A = 0, B = 0 \): \( Y = 0 \cdot 0 = 0 \) (Expected: 1)
- **Conclusion**: AND gate does not satisfy the truth table.

#### Check XNOR Gate
- For \( A = 0, B = 0 \):
- \( \overline{A} = 1, \overline{B} = 1 \)
- \( Y = 0 \cdot 0 + 1 \cdot 1 = 0 + 1 = 1 \) (Expected: 1)
- For \( A = 0, B = 1 \):
- \( Y = 0 \cdot 1 + 1 \cdot 0 = 0 + 0 = 0 \) (Expected: 0)
- For \( A = 1, B = 0 \):
- \( Y = 1 \cdot 0 + 0 \cdot 1 = 0 + 0 = 0 \) (Expected: 0)
- For \( A = 1, B = 1 \):
- \( Y = 1 \cdot 1 + 0 \cdot 0 = 1 + 0 = 1 \) (Expected: 1)
- **Conclusion**: XNOR gate satisfies the truth table.

#### Check XOR Gate
- For \( A = 0, B = 0 \):
- \( Y = 1 \cdot 0 + 0 \cdot 1 = 0 + 0 = 0 \) (Expected: 1)
- **Conclusion**: XOR gate does not satisfy the truth table.

### Final Conclusion
The given truth table corresponds to the **XNOR gate**.

### Summary of Steps:
1. Identify the logic gates and their Boolean expressions.
2. Check each gate against the truth table.
3. Conclude which gate satisfies the truth table.