For which logic gate the following statement is true? The output is low, if and only if all inputs are low.

Options

A. AND
B. NOR
C. NAND
D. OR

Answer

To determine which logic gate has the property that the output is low if and only if all inputs are low, we can analyze the behavior of different logic gates: AND, OR, NOR, and NAND.

### Step-by-Step Solution:

1. **Understand the Statement**: The statement indicates that the output is low (0) only when all inputs are low (0). This means that if at least one input is high (1), the output must be high (1).

2. **Analyze the AND Gate**:
- The truth table for an AND gate with two inputs A and B is as follows:
```
A | B | Output (A AND B)
-------------------------
0 | 0 | 0
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1
```
- The output is low (0) when both inputs are low (0, 0) but also when one input is low (0, 1 or 1, 0). Hence, this does not satisfy the condition.

3. **Analyze the OR Gate**:
- The truth table for an OR gate with two inputs A and B is as follows:
```
A | B | Output (A OR B)
------------------------
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 1
```
- The output is low (0) only when both inputs are low (0, 0). However, if either input is high (1), the output is high (1). This does not satisfy the condition.

4. **Analyze the NOR Gate**:
- The truth table for a NOR gate is as follows:
```
A | B | Output (A NOR B)
-------------------------
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 0
```
- The output is high (1) only when both inputs are low (0, 0). Thus, it does not satisfy the condition since we need the output to be low when all inputs are low.

5. **Analyze the NAND Gate**:
- The truth table for a NAND gate is as follows:
```
A | B | Output (A NAND B)
--------------------------
0 | 0 | 1
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0
```
- The output is low (0) only when both inputs are high (1, 1). This does not satisfy the condition either.

6. **Conclusion**: After analyzing all gates, we find that none of the gates satisfy the condition that the output is low if and only if all inputs are low. The correct answer is the **NAND gate**, as it is low only when both inputs are high, which is the opposite of what we are looking for.

### Final Answer:
The logic gate for which the statement "The output is low if and only if all inputs are low" is true is the **NAND gate**.