The output of an OR gate is connected to both the inputs of a NAND gate. The combination will serve as a

Options

A. NOT gate
B. NOR gate
C. AND gate
D. OR gate

Explanation

To solve the problem, we need to analyze the circuit formed by connecting the output of an OR gate to both inputs of a NAND gate. We will go through the steps systematically.

### Step-by-Step Solution:

1. **Identify the Inputs**:
Let the inputs to the OR gate be A and B.

2. **Determine the Output of the OR Gate**:
The output of the OR gate (let's call it X) can be expressed as:
\[ X = A + B \]
Here, "+" represents the logical OR operation.

3. **Connect the Output of the OR Gate to the NAND Gate**:
The output X from the OR gate is connected to both inputs of the NAND gate. Therefore, the inputs to the NAND gate are X and X.

4. **Determine the Output of the NAND Gate**:
The output of a NAND gate is given by the formula:
\[ Y = \overline{X \cdot X} \]
Since both inputs are the same, we can simplify this to:
\[ Y = \overline{X^2} = \overline{X} \]

5. **Substitute the Output of the OR Gate into the NAND Gate Output**:
Now, substituting the expression for X into the output of the NAND gate:
\[ Y = \overline{A + B} \]

6. **Recognize the Output as a NOR Gate**:
The expression \(\overline{A + B}\) is the definition of a NOR gate. Thus, the output Y represents a NOR operation.

### Conclusion:
The combination of the OR gate followed by the NAND gate serves as a NOR gate.

### Final Answer:
The combination will serve as a NOR gate.

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