If A = {x ∈ ℕ : x is a perfect square}, what type of set is A?
Answer and explanation
Correct answer: An infinite set
The natural-number perfect squares begin 1, 4, 9, 16, 25, and continue as n² for n = 1, 2, 3, and so on. For every natural number n, another perfect square n² can be formed, and there is no greatest natural number. Consequently, A has infinitely many elements and is an infinite set.
Frequently asked questions
What is the correct answer to this question?
An infinite set
Why is this the correct answer?
The natural-number perfect squares begin 1, 4, 9, 16, 25, and continue as n² for n = 1, 2, 3, and so on. For every natural number n, another perfect square n² can be formed, and there is no greatest natural number. Consequently, A has 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.
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