Core XOR property — outputs 1 only when inputs differ: Confirm or reject the statement: “For a two-input XOR gate, the output is 1 only when the inputs are different.”

Introduction / Context:
The exclusive-OR (XOR) gate is central to parity bits, adders (sum without carry), and data encryption primitives because it toggles output when inputs differ. This question checks the canonical verbal definition against the truth table everyone should know.

Given Data / Assumptions:

• Two inputs A and B, positive logic.
• We test the rule “output is 1 only when inputs are different.”
• No timing or analog behavior considered; pure Boolean function.

Concept / Approach:
XOR may be written as A ⊕ B = A′B + AB′. This sum of products turns true exactly for the input pairs 01 and 10 and false for 00 and 11. Thus the statement matches the formal expression and the standard truth table.

Step-by-Step Solution:

Verification / Alternative check:
View XOR as inequality comparator: output = 1 if A ≠ B. In digital comparators, equality output is often implemented as XNOR because XNOR=1 when A=B. This duality verifies the rule by complement.

Why Other Options Are Wrong:

• Incorrect: Contradicts the truth table.
• Negative logic / complementary only / fan-out dependent: Choosing active-low conventions or drive capacity does not change the Boolean truth table.

Common Pitfalls:
Confusing XOR with OR (which is true for 11 as well) or with XNOR (true when inputs are equal). Always anchor to the 4-row truth table to avoid mix-ups.

Final Answer:
Correct