NAND–AND relationship: Assess the claim: “The output of a NAND gate equals the inverted output of an AND gate.” Determine if this statement is accurate for standard positive logic.

Introduction / Context:NAND and AND are complementary operations. Many simplification techniques and universal-gate constructions rely on this exact relationship. Verifying the definition guards against common mistakes when reading mixed NAND/AND schematics or when replacing functions using universal NAND gates.

Given Data / Assumptions:

• Positive logic, two inputs A and B.
• Standard Boolean semantics; no electrical edge cases considered.

Concept / Approach:By definition, NAND(A,B) = NOT(AND(A,B)). In symbolic form: Y_NAND = (A * B)′. Therefore, if Y_AND = A * B, then Y_NAND = NOT(Y_AND). This matches the statement precisely and is true independent of implementation technology (TTL, CMOS, ECL).

Step-by-Step Solution:

Verification / Alternative check:Truth table confirms: AND: 00→0, 01→0, 10→0, 11→1. NAND is the complement: 00→1, 01→1, 10→1, 11→0, which is exactly the inversion of AND’s output row by row.

Why Other Options Are Wrong:

• Incorrect or technology-limited options: Boolean identity does not depend on output topology or supply voltage; it is logically universal.

Common Pitfalls:Mixing up NAND with NOR (the complement of OR). Remember: NAND complements AND; NOR complements OR.

Final Answer:Correct