The Boolean expression `P+bar(P)Q`, where P and Q are the inputs of the logic circuit, represents

Options

A. AND gate
B. NAND gate
C. NOT gate
D. OR gate

Answer

To solve the Boolean expression \( P + \overline{P}Q \) and determine which logic gate it represents, we can follow these steps:

### Step 1: Understand the components of the expression
The expression consists of two variables, \( P \) and \( Q \), and involves the NOT operation (represented by \( \overline{P} \)) and the OR operation (represented by \( + \)). The term \( \overline{P}Q \) represents the AND operation between \( \overline{P} \) and \( Q \).

### Step 2: Create a truth table
We will create a truth table for the inputs \( P \) and \( Q \) to evaluate the expression \( P + \overline{P}Q \).

| \( P \) | \( Q \) | \( \overline{P} \) | \( \overline{P}Q \) | \( P + \overline{P}Q \) |
|---------|---------|---------------------|---------------------|--------------------------|
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |

### Step 3: Analyze the output column
From the truth table, we can observe the output of \( P + \overline{P}Q \):
- When \( P = 0 \) and \( Q = 0 \), the output is 0.
- When \( P = 0 \) and \( Q = 1 \), the output is 1.
- When \( P = 1 \) and \( Q = 0 \), the output is 1.
- When \( P = 1 \) and \( Q = 1 \), the output is 1.

### Step 4: Identify the logic gate
The output of the expression \( P + \overline{P}Q \) is 1 in all cases except when both \( P \) and \( Q \) are 0. This behavior matches that of an OR gate, which outputs 1 if at least one of its inputs is 1.

### Conclusion
The Boolean expression \( P + \overline{P}Q \) represents an OR gate.