Evaluate the statement: "A NOR gate is a universal gate," meaning it alone can be composed to realize any Boolean function.

Introduction / Context:
Universal gates are gate types from which any Boolean function can be constructed without requiring additional primitive gates. Understanding which families are universal informs design choices, minimization, and library constraints.

Given Data / Assumptions:

• NOR is defined as NOT(OR).
• We can freely interconnect multiple NOR gates.
• Inverter behavior can be synthesized from a NOR gate by tying its inputs together.

Concept / Approach:
NOR is universal because you can build NOT, OR, and AND using only NOR gates. Once those primitives are available, arbitrary combinations (SOP, POS, and multi-level networks) can be constructed to realize any Boolean expression. The dual universal gate is NAND, which similarly suffices for complete logic construction.

Step-by-Step Solution:
1) NOT from NOR: Y = NOR(A, A) = NOT(A OR A) = NOT A.2) OR from NOR: Use De Morgan transformations; OR can be achieved via inverted inputs to a NOR, implemented with additional NOR inverters.3) AND from NOR: A AND B = NOT(NOT A OR NOT B). Using NOR-based inverters and one NOR, we realize AND.4) With NOT/AND/OR available, arbitrary Boolean functions follow.

Verification / Alternative check:
Standard logic textbooks provide canonical constructions for NOT, OR, and AND from NOR, proving universality.

Why Other Options Are Wrong:
“Incorrect” contradicts established theory. “Only universal with XOR present” is unnecessary; XOR itself can be built from NORs. “Universal only for two-level SOP” is too restrictive; multi-level implementations are also possible with NOR-only networks.

Common Pitfalls:
Assuming universality requires a special gate like XOR; forgetting that tying inputs together yields inversion with NOR.

Final Answer:
Correct