To determine the correct answer regarding the logic gates X and Y, let's analyze each option in detail, focusing on the properties of logic gates and their outputs based on input states. Correct Option: B. The output state of each depends on the input state Explanation of Why Option B is Correct:

1. Understanding Logic Gates: Logic gates are fundamental building blocks in digital circuits. They perform basic logical functions that are essential for digital circuits. The output of a logic gate is determined by its input states according to specific logical rules.
2. Input-Output Relationship: For any logic gate, the output is a direct result of the inputs provided. For example, in a simple AND gate, the output is true (1) only when all inputs are true (1). In contrast, an OR gate outputs true if at least one input is true. This dependency on input states is a defining characteristic of all logic gates.
3. Generalization: Since the question refers to both gates X and Y, we can conclude that both gates will have outputs that depend on their respective inputs. This is true for any logic gate, making option B universally applicable.

Why the Other Options are Incorrect: Option A: They both have multiple output variables

• Explanation: This statement is misleading because not all logic gates have multiple outputs. Most basic logic gates (like AND, OR, NOT) have a single output. While there are gates like multiplexers or decoders that can have multiple outputs, the question does not specify that X and Y are such gates. Therefore, without additional context, we cannot assume they both have multiple outputs.

Option C: The output is true only if all inputs are true

• Explanation: This statement describes the behavior of an AND gate specifically. However, it does not apply to all logic gates. For instance, an OR gate outputs true if at least one input is true, and a NOT gate outputs the opposite of its single input. Since we do not know the specific types of gates X and Y, we cannot assert that this statement is universally true for both.

Option D: They are both equivalent gates

• Explanation: For two gates to be equivalent, they must produce the same output for all possible input combinations. Without knowing the specific types of gates X and Y, we cannot conclude that they are equivalent. They could be different types of gates (e.g., one could be an AND gate and the other an OR gate), which would make them non-equivalent.

Summary of Key Points:

• Logic gates produce outputs based on their input states, making option B the correct choice.
• Not all logic gates have multiple outputs (Option A is incorrect).
• The statement about outputs being true only if all inputs are true (Option C) is specific to AND gates and does not apply universally.
• Without specific information, we cannot assume that two gates are equivalent (Option D is incorrect).

Revision Summary:

• Logic gates' outputs depend on their inputs.
• Basic gates typically have a single output.
• The behavior of gates varies (AND, OR, NOT), so general statements may not apply.
• Equivalence between gates requires specific conditions that are not guaranteed without further information.