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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

Which of the following is the set-builder form of the set A = {1, 4, 9, 16, 25}?

The set {1, 4, 9, 16, 25} consists of the squares of the natural numbers 1 to 5, so its set-builder form is {x² : x is a natural number and x ≤ 5}. The other forms generate different elements or infinitely many elements.

  1. A{x : x is a natural number and x ≤ 25}
  2. B{x² : x is a natural number and x ≤ 5}Correct
  3. C{2x : x is a natural number and x ≤ 5}
  4. D{x² : x is an integer and x ≤ 5}

Explanation

The elements 1, 4, 9, 16, 25 are the squares of 1, 2, 3, 4, 5. So A = {x² : x ∈ N, x ≤ 5}. Option C gives 2, 4, 6, 8, 10. Option D includes all integers up to 5, so it would contain 0, 4, 9... for negatives and infinitely many elements, which is wrong.

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