Logic family transformation: what Boolean function results when you append a NOT (inverter) to the output of an AND gate, creating a single composite gate?

Introduction / Context:
Combining basic gates yields new, widely used logic functions. By inverting the output of a gate, you form the complemented function. Understanding these compositions is important because NAND and NOR are universal gates, enabling the construction of any logic function using only one gate type.

Given Data / Assumptions:

• Start with an AND gate producing Y = A * B (for two inputs; generalizes to more).
• Add a NOT gate to the output, so output becomes Y′ = NOT(Y).
• We must name the resulting composite function.

Concept / Approach:
By definition, NAND (Not-AND) is the logical complement of AND. If AND outputs 1 only when all inputs are 1, then NAND outputs 0 only when all inputs are 1 and 1 otherwise. This simple inversion transforms the behavior and yields a gate that is functionally complete for digital design.

Step-by-Step Solution:
Express AND: Y = A * B.Invert output: Z = NOT(Y) = NOT(A * B).Recognize Z as the NAND function.Select “NAND.”

Verification / Alternative check:
Truth table check confirms: AND truth table inverted equals NAND truth table. NAND is a universal gate used to implement NOT, AND, OR, XOR, and more through combinations.

Why Other Options Are Wrong:
OR: requires different input combination, not a simple inversion of AND.XOR: equality-based function; not obtained by inverting AND.NOR: inversion of OR, not AND.None: incorrect because NAND is correct.

Common Pitfalls:
Confusing NAND and NOR; forgetting that “complementing the output” means invert the entire function result, not each input.

Final Answer:
NAND