K-map grouping rules: “Single looping in groups of three is a common Karnaugh-map simplification technique.” Evaluate this claim about allowed group sizes in K-map minimization.

Introduction / Context:
Karnaugh maps (K-maps) are used to group adjacent 1-cells (for SOP) or 0-cells (for POS) to reduce Boolean expressions. The rules for legal group sizes are central to obtaining correct simplified results.

Given Data / Assumptions:

• We are considering standard K-maps for 2–6 variables.
• Groups must be rectangular and contain 1, 2, 4, 8, 16, ... cells.
• Wrap-around adjacency applies across map edges due to Gray code ordering.

Concept / Approach:
Legal groups always have sizes that are powers of two. Grouping in threes is not permitted because it does not eliminate a consistent set of variables, and it cannot represent a valid implicant in minimized SOP/POS. Allowed group sizes correspond to removing one, two, three, or more variables per group, each time halving the number of fixed literals.

Step-by-Step Solution:

Verification / Alternative check:
Try to write a product term for a supposed 3-cell group; one variable will flip within the group, defeating elimination and proving it is not a valid implicant.

Why Other Options Are Wrong:
“Correct” contradicts K-map fundamentals. References to don’t-care or POS do not legalize 3-sized groups; even with don’t-care cells, final chosen groups must still be powers of two.

Common Pitfalls:
Attempting irregular shapes, ignoring wrap-around adjacency, or choosing many small groups instead of fewer larger groups.

Final Answer:
Incorrect