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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