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

Difficulty: Easy

Correct Answer: Set of all concentric circles

Explanation:


Introduction / Context:
An infinite set has no finite bound on its elements. Geometric constructions often yield infinite families (e.g., circles with the same center and varying radii).



Given Data / Assumptions:

  • Even prime numbers: only {2} (finite)
  • Rivers in one country: finite list
  • Concentric circles about a fixed center: radius can vary over infinitely many positive values


Concept / Approach:
Check whether there is a natural limiting count. Concentric circles admit unboundedly many radii.



Step-by-Step Solution:
(a) = {2} → finite(b) Finite by geography(c) Infinite family by any distinct positive radius



Verification / Alternative check:
Between any two radii, more radii exist (continuum), reinforcing infinitude.



Why Other Options Are Wrong:
They are finite sets by definition or context.



Common Pitfalls:
Misinterpreting 'even prime' as many primes; there is only one even prime.



Final Answer:
Set of all concentric circles

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