Relationship between AND and NAND outputs: Across all possible input combinations, the output of a NAND gate is the logical inversion (complement) of the output of an AND gate driven by the same inputs. Assess this statement.

Introduction / Context: AND and NAND are tightly linked: a NAND is an AND with an inversion at its output. Recognizing this relationship helps with quick truth-table derivations, hardware substitutions, and De Morgan transformations when optimizing logic.

Given Data / Assumptions:

• We compare a two-input AND gate and a two-input NAND gate with the same inputs.
• Logic abstraction (no timing hazards) applies.
• Standard Boolean operations and identities are used.

Concept / Approach: Define the functions: AND output is F = A · B. NAND output is G = NOT(A · B). Clearly, G = NOT(F). Therefore, for each input pair, the NAND’s output is the complement of the AND’s output. This holds for all combinations: 00, 01, 10 produce F=0 → G=1; 11 produces F=1 → G=0.

Step-by-Step Solution:

Verification / Alternative check: Create a small table: inputs 00,01,10 → F=0 so G=1; input 11 → F=1 so G=0. Every row shows inversion, confirming the statement conclusively.

Why Other Options Are Wrong: “Incorrect” contradicts the formal definitions. Claims about rise times or logic families (TTL vs CMOS) concern implementation details and do not alter the Boolean relationship.

Common Pitfalls: Forgetting that NAND is simply AND plus an output inversion; mixing up NAND with NOR (which is the inversion of OR).

Final Answer: Correct