Form classification check: Consider the Boolean expression (A + B) * (C + D’). Decide whether classifying it as a product-of-sums (POS) expression is correct.

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:

  • Expression under review: (A + B) * (C + D’).
  • Operator conventions: + denotes OR, * denotes AND, ’ denotes NOT.
  • Each parenthesized term is a sum (OR) of literals.


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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