If N₁ = {x : x ∈ ℕ, x² ≤ 10} and O₁ = {1, 2, 3}, which statement is correct?
Answer and explanation
Correct answer: N₁ = O₁
For natural numbers, evaluate x² ≤ 10. The values x = 1, 2, and 3 work because their squares are 1, 4, and 9. The next natural number, 4, does not work because 4² = 16, which is greater than 10. Thus N₁ = {1, 2, 3}. This is exactly O₁, so the correct statement is N₁ = O₁. The inclusive sign ≤ does not add 4 because no natural-number square equals 10.
Frequently asked questions
What is the correct answer to this question?
N₁ = O₁
Why is this the correct answer?
For natural numbers, evaluate x² ≤ 10. The values x = 1, 2, and 3 work because their squares are 1, 4, and 9. The next natural number, 4, does not work because 4² = 16, which is greater than 10. Thus N₁ = {1, 2, 3}. This is exactly O₁, so the correct statement is N₁ = O₁. The inclusive sign ≤ does not add 4 because no natural-number square equals 10.
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.
