Identify the finite set among descriptions: Which of the following sets is finite?

Introduction / Context:Finite vs infinite sets is a foundational classification. Sets defined by bounded inequalities over natural numbers are finite; sets described by open-ended rules typically are infinite.

Given Data / Assumptions:

• N denotes positive integers
• Quadrilaterals on a plane can vary continuously
• Primes and multiples extend without bound

Concept / Approach:Translate each description and determine whether it yields finitely many elements.

Step-by-Step Solution:(a) Primes: infinite set(b) Quadrilaterals in the plane: uncountably many (varying side lengths and angles)(c) x^2 ≤ 25 with x ∈ N → x ∈ {1,2,3,4,5} (finite)(d) Multiples of 3 in N: infinite

Verification / Alternative check:Count in (c) is 5 elements, confirming finiteness.

Why Other Options Are Wrong:They describe sets with endlessly many elements by rule or continuous variation.

Common Pitfalls:Including 0 in N; even then, (c) remains finite.

Final Answer:{x: x ∈ N and x^2 − 25 ≤ 0}