Boolean product evaluation: Confirm the fundamental identity 1 · 0 = 0 in Boolean algebra, where “·” denotes logical AND.

Introduction / Context: Boolean algebra underpins digital logic. The AND operation corresponds to multiplication-like behavior where the result is true only if all operands are true. Verifying basic identities like 1 · 0 = 0 ensures accurate reasoning about gates and circuits.

Given Data / Assumptions:

• Binary values use 1 for HIGH/true and 0 for LOW/false.
• AND truth: true only when both inputs are true.
• We are working at the logical, not analog, level.

Concept / Approach: By the AND definition, if any input is 0, the output must be 0. Therefore, 1 AND 0 is 0, and 0 AND 1 is 0, and 0 AND 0 is 0. Only 1 AND 1 yields 1. These form the core truth table reflected in gate behavior and in Boolean equations.

Step-by-Step Solution:

Verification / Alternative check: Truth table check: rows (1,0) and (0,1) both give 0. Algebraic properties (annihilator for AND) also state that 0 is the absorbing element: X · 0 = 0 for any X.

Why Other Options Are Wrong: “Incorrect” contradicts the AND definition. “Only true in arithmetic” misunderstands the mapping between Boolean AND and multiplication-like behavior. “Depends on voltage thresholds” addresses implementation details, not the abstract Boolean law.

Common Pitfalls: Mixing arithmetic and logic but forgetting the identical outcome for this specific case; considering analog exceptions that are beyond Boolean abstraction.

Final Answer: Correct