Truth-table complement – is a NOR gate's output the logical complement of an OR gate's output for the same inputs?

Introduction / Context:
OR and NOR are complementary logic functions. Recognizing how one relates to the other is essential when switching between active-HIGH and active-LOW conventions and when reading symbols that include inversion bubbles.

Given Data / Assumptions:

• Inputs are identical for both OR and NOR comparisons.
• Active-HIGH logic levels and ideal Boolean behavior are assumed.
• No consideration of propagation delay or analog drive strength is required.

Concept / Approach:
By definition, NOR(A,B,...) = NOT(OR(A,B,...)). Therefore, for every input combination, the NOR output bit is exactly the inversion of the OR output bit. This is what it means for the truth table to be the “opposite” or complement—each row's output is flipped between the two gates.

Step-by-Step Solution:

Verification / Alternative check:
Consider two inputs: OR truth table is 00→0, 01→1, 10→1, 11→1; NOR is 00→1, 01→0, 10→0, 11→0—a perfect complement across all rows. Symbols also show an inversion bubble at the NOR output, signaling the negation.

Why Other Options Are Wrong:
“Incorrect” contradicts the formal definition. Conditions about open-collector outputs or DC operation are irrelevant to the Boolean complement relationship.

Common Pitfalls:
Misreading schematic bubbles or assuming that hardware packaging changes logic definition. Hardware details affect electrical behavior, not truth-table identity.

Final Answer:
Correct