Identifying canonical forms: Which Boolean output expression is explicitly in product-of-sums (POS) form, indicating an implementation as an AND of OR terms?

Introduction / Context:
Digital designers often express logic functions in canonical or standard forms to map them to gate-level structures. Two widely used forms are sum-of-products (SOP) and product-of-sums (POS). Recognizing POS is key when you plan to realize a function using OR gates feeding an AND gate (or NAND–NAND with DeMorgan equivalents).

Given Data / Assumptions:

• SOP means OR of AND terms (e.g., AB + ĀC).
• POS means AND of OR terms (e.g., (A + B)(Ā + C)).
• Variables may appear complemented (with a bar) or uncomplemented.

Concept / Approach:
To classify an expression, look at the outermost operator. If the outermost operator is AND (a product) and its factors are sums (OR groupings inside parentheses), the expression is in POS form. Conversely, if the outermost operator is OR and the terms inside are products (concatenations), the expression is SOP.

Step-by-Step Solution:
Inspect option a: Y = (A + B)(Ā + C). Outermost operator is multiplication; each factor is an OR term → POS.Inspect option b: Y = AB + ĀC. Outermost operator is addition; terms are products → SOP, not POS.Inspect option c: Y = (A B)(C + D) mixes a product term (A B) with a sum; not canonical POS.Inspect option d: Y = A + B + C is a simple sum, not a product of sums.

Verification / Alternative check:
Gate mapping: POS maps to OR gates feeding a final AND. Option a naturally synthesizes as two OR gates whose outputs are ANDed, confirming the POS structure.

Why Other Options Are Wrong:
AB + ĀC: clear SOP.(A B)(C + D): first factor is not a sum; not POS.A + B + C: no AND of sums.

Common Pitfalls:
Judging by appearance rather than the outermost operator hierarchy. Always check whether sums are being multiplied (POS) or products are being added (SOP).

Final Answer:
Y = (A + B)(Ā + C)