In which option are both sets infinite?
Answer and explanation
Correct answer: {x ∈ ℕ : x > 100} and {x ∈ ℤ : x < 0}
The natural numbers greater than 100 are 101, 102, 103, and so on without end, so the first set in option B is infinite. The negative integers less than zero are −1, −2, −3, and so on, which also continue indefinitely; therefore the second set is infinite. The other options contain bounded sets, divisors of 100, or sets with only zero or one element.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℕ : x > 100} and {x ∈ ℤ : x < 0}
Why is this the correct answer?
The natural numbers greater than 100 are 101, 102, 103, and so on without end, so the first set in option B is infinite. The negative integers less than zero are −1, −2, −3, and so on, which also continue indefinitely; therefore the second set is infinite. The other options contain bounded sets, divisors of 100, or sets with only zero or one element.
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.
