Identify the finite set among descriptions: Which of the following sets is finite?
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A{x: x ∈ N and x is a prime number}
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B{x: x is a quadrilateral on a plane}
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C{x: x ∈ N and x^2 − 25 ≤ 0}
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D{x: x ∈ N and x is a multiple of 3}
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ENone of these
Answer
Correct Answer: {x: x ∈ N and x^2 − 25 ≤ 0}
Explanation
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}