Difficulty: Easy
Correct Answer: Correct
Explanation:
Introduction / Context: Boolean expressions are commonly written in canonical or standard forms. Two key forms are sum-of-products (SOP) and product-of-sums (POS). Being able to recognize these patterns is essential for mapping to AOI/OAI structures and for minimization with K-maps or algebraic methods.Given Data / Assumptions:
Concept / Approach: A product-of-sums (POS) is an AND of sum terms. Each sum term is an OR of literals. In this case, (A + B) is a sum term, and (C + D’) is another sum term; their AND constitutes a POS expression. In contrast, SOP is an OR of product terms such as AB + CD’.Step-by-Step Solution:
Identify sums: S1 = (A + B), S2 = (C + D’).Combine by product: S1 * S2 — an AND of sums.Definition alignment: AND of sums ⇒ POS.Therefore, the classification as POS is correct.Verification / Alternative check:
Distribute to SOP equivalence if needed: (A + B)(C + D’) = AC + AD’ + BC + BD’, confirming it is an AND of sum terms before distribution.Why Other Options Are Wrong:
Incorrect / SOP / Neither: They contradict the structural definition of POS as an AND of sum terms.Common Pitfalls:
Confusing operator precedence or notation conventions.Assuming complements invalidate form classification; complements within sums are allowed.Final Answer:
Correct
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