If E₁ = {x : x ∈ ℕ, x² ≤ 100, and x is odd}, which is E₁ in roster form?
Answer and explanation
Correct answer: E₁ = {1, 3, 5, 7, 9}
Because x is a natural number, x is non-negative; the inequality x² ≤ 100 gives x ≤ 10. The natural numbers from 1 through 10 that are odd are 1, 3, 5, 7, and 9. The number 11 is excluded because its square is greater than 100, and even numbers do not satisfy the oddness condition. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
E₁ = {1, 3, 5, 7, 9}
Why is this the correct answer?
Because x is a natural number, x is non-negative; the inequality x² ≤ 100 gives x ≤ 10. The natural numbers from 1 through 10 that are odd are 1, 3, 5, 7, and 9. The number 11 is excluded because its square is greater than 100, and even numbers do not satisfy the oddness condition. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
