The correct option for the truth table provided is D. NAND logic gate. Let's break down the reasoning step-by-step. Step-by-Step Explanation

1. Understanding the Truth Table: The truth table shows three columns: P, O, and R. The first two columns (P and O) represent the inputs, while the last column (R) represents the output. The values in the table are as follows:

| P | O | R | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 0 |

1. Analyzing the Output: To determine which logic gate this truth table represents, we need to analyze the output (R) based on the inputs (P and O):
2. When both inputs are 0 (P=0, O=0), the output is 1 (R=1).
3. When the first input is 0 and the second input is 1 (P=0, O=1), the output is 0 (R=0).
4. When the first input is 1 and the second input is 0 (P=1, O=0), the output is 0 (R=0).
5. When both inputs are 1 (P=1, O=1), the output is 0 (R=0).
6. Identifying the Logic Gate:
7. NAND Gate: The NAND (Not AND) gate outputs 0 only when both inputs are 1. In all other cases, it outputs 1. This matches our truth table:
   • For (0, 0) → R = 1
   • For (0, 1) → R = 0
   • For (1, 0) → R = 0
   • For (1, 1) → R = 0
8. Therefore, the truth table corresponds to a NAND gate.

Why Other Options Are Incorrect

• A. NOT Logic Gate:
• A NOT gate has only one input and inverts it. The truth table for a NOT gate would look like this: | Input | Output | |-------|--------| | 0 | 1 | | 1 | 0 |
• Since our truth table has two inputs, this option is not applicable.
• B. NOR Logic Gate:
• A NOR gate outputs 1 only when both inputs are 0. The truth table for a NOR gate would look like this: | P | O | R | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 0 |
• While the first row matches, the output for (1, 0) and (0, 1) does not match the NOR gate's behavior, making this option incorrect.
• C. AND Logic Gate:
• An AND gate outputs 1 only when both inputs are 1. The truth table for an AND gate would look like this: | P | O | R | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |
• This does not match our truth table at all, so this option is also incorrect.

Summary of Key Points

• The truth table provided corresponds to a NAND gate.
• A NAND gate outputs 1 when at least one input is 0 and outputs 0 only when both inputs are 1.
• The other options (NOT, NOR, AND) do not match the output behavior of the truth table.
• Understanding the behavior of basic logic gates is crucial for interpreting truth tables correctly.

This thorough analysis should help you understand how to approach similar questions in the future!