If N₁ = {x : x is a perfect-square natural number}, what type of set is N₁?
Answer and explanation
Correct answer: Infinite set
The perfect-square natural numbers begin as 1, 4, 9, 16, 25, and continue as 36, 49, 64, and so on. For every natural number n, the number n² is a perfect square, and there is no largest natural number. Consequently, new perfect squares continue without end, so N₁ contains infinitely many elements and is an infinite set.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
The perfect-square natural numbers begin as 1, 4, 9, 16, 25, and continue as 36, 49, 64, and so on. For every natural number n, the number n² is a perfect square, and there is no largest natural number. Consequently, new perfect squares continue without end, so N₁ contains infinitely many elements and is an infinite set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
