Which set is finite even though listing its elements may be long?
Answer and explanation
Correct answer: {x ∈ N : x is prime and x < 1000}
There are only finitely many natural numbers less than 1000, namely the numbers from 1 through 999. The prime numbers satisfying the condition form a subset of this finite collection, so their number is also finite, even though the list may be fairly long. In contrast, there are infinitely many natural primes, infinitely many negative integers, and infinitely many real numbers between 0 and 1. Therefore option B is the finite set.
Frequently asked questions
What is the correct answer to this question?
{x ∈ N : x is prime and x < 1000}
Why is this the correct answer?
There are only finitely many natural numbers less than 1000, namely the numbers from 1 through 999. The prime numbers satisfying the condition form a subset of this finite collection, so their number is also finite, even though the list may be fairly long. In contrast, there are infinitely many natural primes, infinitely many negative integers, and infinitely many real numbers between 0 and 1. Therefore option B is the finite set.
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.
