To determine which logic gate gives an output that is opposite to the input state, we need to understand the behavior of different types of logic gates. The most common logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Among these, the gate that specifically outputs the opposite of the input state is the NOT gate. Step-by-Step Explanation:

1. Understanding Logic Gates:
2. AND Gate: Outputs true (1) only if all inputs are true (1).
3. OR Gate: Outputs true (1) if at least one input is true (1).
4. NOT Gate: Outputs the opposite of the input. If the input is true (1), the output is false (0), and vice versa.
5. NAND Gate: Outputs false (0) only if all inputs are true (1); otherwise, it outputs true (1).
6. NOR Gate: Outputs true (1) only if all inputs are false (0).
7. XOR Gate: Outputs true (1) if the inputs are different.
8. XNOR Gate: Outputs true (1) if the inputs are the same.
9. Identifying the NOT Gate:
10. The NOT gate is the only gate that inverts the input. For example:
    • If the input is 0, the output is 1.
    • If the input is 1, the output is 0.
11. This characteristic makes the NOT gate the correct answer to the question of which gate gives an output opposite to the input state.
12. Analyzing the Options:
13. Option A: X - If X is a NOT gate, this option is correct.
14. Option B: Y - If Y is not a NOT gate, this option is incorrect.
15. Option C: Z - If Z is not a NOT gate, this option is incorrect.
16. Option D: X and Y - This option suggests that both X and Y are NOT gates, which is incorrect if only one of them is.
17. Conclusion:
18. Since the NOT gate is the only gate that outputs the opposite of the input state, if option A corresponds to a NOT gate, then it is indeed the correct answer.

Why Other Options Are Incorrect:

• Option B (Y): If Y is an AND, OR, or any other gate that does not invert the input, it cannot be the correct answer.
• Option C (Z): Similar reasoning applies; if Z is not a NOT gate, it cannot provide the opposite output.
• Option D (X and Y): This option implies that both gates must be NOT gates, which is not possible if only one of them is.

Revision Summary:

• The NOT gate is the only logic gate that outputs the opposite of the input state.
• Other gates (AND, OR, NAND, NOR, XOR, XNOR) do not invert the input.
• Always analyze the function of each gate to determine its output based on the input.
• In questions about logic gates, identifying the NOT gate is crucial for finding the correct answer.