If A = {x ∈ N : x² ≤ 30 and x is odd}, how many elements does A contain?
Answer and explanation
Correct answer: 3
For natural numbers, x² ≤ 30 implies x ≤ √30, and √30 is approximately 5.47. Therefore, the possible natural numbers are 1, 2, 3, 4, and 5. The odd numbers among them are 1, 3, and 5, so A = {1, 3, 5}. This set contains three elements. The correct answer is option B; the count must be made after applying both the square bound and the odd-number condition.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For natural numbers, x² ≤ 30 implies x ≤ √30, and √30 is approximately 5.47. Therefore, the possible natural numbers are 1, 2, 3, 4, and 5. The odd numbers among them are 1, 3, and 5, so A = {1, 3, 5}. This set contains three elements. The correct answer is option B; the count must be made after applying both the square bound and the odd-number condition.
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.
