Let A = {x ∈ ℕ : x is a perfect square and x < 50}. How many elements does A have?
Answer and explanation
Correct answer: 7
The governing concept is counting the elements of a finite set under an upper bound. The natural-number perfect squares below 50 are 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, and 7² = 49. The next square, 8² = 64, is not less than 50. Thus A has 7 elements, making option B correct. The bound prevents the set from being infinite.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The governing concept is counting the elements of a finite set under an upper bound. The natural-number perfect squares below 50 are 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, and 7² = 49. The next square, 8² = 64, is not less than 50. Thus A has 7 elements, making option B correct. The bound prevents the set from being infinite.
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.
