Boolean complement rule: Evaluate the statement: “In Boolean algebra, the complement of 1 is 0.” Support your answer with truth-level reasoning.

Introduction / Context:Complements are fundamental in Boolean algebra and digital logic. The complement (logical NOT) flips a truth value: what is true becomes false and vice versa. This concept is directly realized in hardware by inverters.

Given Data / Assumptions:

• Binary logic levels: 0 and 1 represent false and true, respectively.
• NOT operation: produces the complement of its input.
• Positive logic is assumed (1 = TRUE, 0 = FALSE).

Concept / Approach:By the definition of complement in Boolean algebra, NOT(1) = 0 and NOT(0) = 1. This identity underlies De Morgan’s laws, inverter gates, and expressions using overbars or primes.

Step-by-Step Solution:

Verification / Alternative check:Truth table of an inverter: input 0 → output 1; input 1 → output 0. The mapping is unambiguous.

Why Other Options Are Wrong:

Common Pitfalls:Confusing logic polarity (active-HIGH/LOW) with the meaning of NOT; assuming electrical inversion always implies voltage inversion rather than logic inversion.

Final Answer:Correct