Boolean forms — identifying product-of-sums (POS) Which of the following Boolean expressions is written in canonical product-of-sums (sum terms multiplied together) form?

Introduction / Context:Digital logic expressions are often represented in standardized forms to simplify analysis and implementation. Two common normalized styles are sum-of-products (SOP) and product-of-sums (POS). Being able to recognize POS at a glance is fundamental for Karnaugh-map simplification, gate-level realization, and understanding how OR and AND operators structure a logic function.

Given Data / Assumptions:

• We compare four candidate expressions.
• Notation: + denotes OR; juxtaposition (e.g., AB) denotes AND.
• POS means a product (AND) of sum terms (ORs of literals).

Concept / Approach:In POS, the overall expression is an AND of terms, where each term is an OR of literals, such as (A + B + C)(A' + D). In contrast, SOP is an OR of AND terms, such as AB + A'C. By inspecting parentheses and operators, we can classify each option quickly without full expansion.

Step-by-Step Solution:

Verification / Alternative check:Expand option (a) using distributive property to show it becomes an OR of multiple product terms—consistent with POS expanded form.

Why Other Options Are Wrong:

• (AB)(CD): lacks sum terms inside parentheses.
• AB(CD): no OR inside the factors, therefore not POS.
• AB + CD: this is SOP (sum of products), not product of sums.

Common Pitfalls:Confusing the outer operator with the inner one; in POS, the outermost operator is AND, and each parenthesized factor must contain an OR of literals.

Final Answer:(A + B)(C + D)