Canonical SOP restriction: In a true sum-of-products (SOP) expression, inversion (complement) bars apply to individual variables only, not across sums of variables. Is this statement valid for canonical SOP forms?

Introduction / Context:
Boolean expressions can be written in different canonical and standard forms, notably sum-of-products (SOP) and product-of-sums (POS). Understanding how complements appear in each form helps prevent algebraic mistakes and leads to correct gate-level implementations.

Given Data / Assumptions:

• We are discussing true or canonical SOP, where each product term is a conjunction of literals.
• A literal is either a variable (e.g., A) or its complement (A’).
• No overbar should span a sum inside an SOP product term.

Concept / Approach:
In SOP, each term is an AND of literals, and the overall function is an OR of those terms. Complements apply to individual variables within product terms, not to grouped sums. An overbar spanning a sum indicates a complemented sum, which belongs to POS or requires application of De Morgan’s theorems to return to SOP.

Step-by-Step Solution:

Verification / Alternative check:
Construct a Karnaugh map and derive the minimal SOP. The grouped cells correspond to product terms with complements on variables only, never complemented sums within a product term.

Why Other Options Are Wrong:

• Incorrect/conditional options: The rule is general to SOP structure, independent of the number of variables or gate technology.

Common Pitfalls:
Mixing SOP and POS conventions; placing bars over entire parentheses in SOP; forgetting to transform complemented sums using De Morgan’s laws.

Final Answer:
Correct