K-map yields a minimized Boolean equation: A correctly completed Karnaugh map (K-map) always allows derivation of a simplified Boolean equation by grouping adjacent cells in powers of two and eliminating changing variables. Judge this general statement.

Introduction / Context: K-maps provide a graphical method for simplifying Boolean expressions. They help designers reduce logic by combining adjacent minterms (for SOP) or maxterms (for POS) into larger implicants, directly producing a minimized or near-minimized Boolean equation.

Given Data / Assumptions:

• Proper K-map layout using Gray coding for variable ordering.
• Valid entries: 1s (minterms), 0s, and optional don’t-care (X) cells.
• Grouping rules: rectangles of size 1, 2, 4, 8, ... with wrap-around adjacency.

Concept / Approach: By grouping adjacent 1s for SOP (or 0s for POS), variables that change within the group are eliminated from the product (or sum) term, yielding simpler expressions. Don’t-care cells can be used to enlarge groups, further simplifying the final equation.

Step-by-Step Solution:

Verification / Alternative check: Compare the derived equation against algebraic simplification or Quine–McCluskey results for the same function. The K-map approach should match or closely approximate the minimum form.

Why Other Options Are Wrong: It is not limited to three variables; 2–6 variable maps are standard. The presence or absence of don’t-cares does not prevent simplification; it often helps.

Common Pitfalls: Making non-rectangular groups, ignoring wrap-around adjacency, or using non-power-of-two group sizes.

Final Answer: Correct