Gate universality and functional completeness: Determine whether one can build a logical AND function using only NOR gates (i.e., express A * B solely with NORs).

Introduction / Context:
NOR and NAND gates are universal, meaning any Boolean function can be implemented using only one of these gate types. Understanding equivalences via De Morgan’s theorems is a staple of digital logic design and optimizations in standard-cell libraries.

Given Data / Assumptions:

• Target: implement AND using only NOR.
• Available primitive: 2-input NOR (and inverter via tying inputs).
• Boolean identities and De Morgan’s laws are applicable.

Concept / Approach:
From De Morgan: A * B = (A' * B') = (A' + B')'. A NOR gate computes (X + Y)'. If we can obtain A' and B', then a single NOR of A' and B' yields (A' + B')' = A * B. Inverters can be made by tying both inputs of NOR together (X NOR X = X').

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