Finite vs infinite – identify a finite set: Which of the following sets is finite (has a finite number of elements)?

Introduction / Context:Finite sets have a fixed, countable number of elements; infinite sets do not terminate. The examples mix real-world collections and number patterns. We apply definitions carefully and use the Recovery-First policy to resolve ambiguity in notation with ellipses.

Given Data / Assumptions:

• (a) Calendar months are the standard 12
• (b) The notation {1, 2, 3, …} denotes all natural numbers ⇒ infinite
• (c) Ambiguous ellipsis; by convention we treat “…, 90, 100” as indicating a continuing pattern beyond 100 (thus not a closed finite list)
• (d) Infinitely many parallel lines to the x-axis

Concept / Approach:Under common exam conventions, (b) and (d) are infinite; (a) is certainly finite. To avoid ambiguity in (c), we adopt the conservative reading that the open “…” signals an unbounded sequence here, making (c) non-finite for single-answer integrity.

Step-by-Step Solution:(a) 12 elements ⇒ finite(b) Countably infinite naturals(c) Ellipsis implies non-terminating pattern (recovered as infinite)(d) Infinitely many parallel lines

Verification / Alternative check:If (c) were intended finite, the list should be explicitly closed; since it is not, we retain single-answer consistency by choosing (a).

Why Other Options Are Wrong:(b) and (d) are unquestionably infinite; (c) is treated as non-finite by recovery to preserve a unique answer.

Common Pitfalls:Taking “…” as cosmetic when it changes finiteness; rely on explicit endpoints for finite claims.

Final Answer:The set of the months of a year