If A = {x : x ∈ ℕ, x is a prime number greater than 20}, what kind of set is A?
Answer and explanation
Correct answer: Infinite set
The set contains primes such as 23, 29, 31, 37, and many more. There is no largest prime number; Euclid’s theorem establishes that infinitely many prime numbers exist. Removing the finitely many primes that are at most 20 still leaves infinitely many primes greater than 20. Therefore A is an infinite set, not a finite or singleton set.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
The set contains primes such as 23, 29, 31, 37, and many more. There is no largest prime number; Euclid’s theorem establishes that infinitely many prime numbers exist. Removing the finitely many primes that are at most 20 still leaves infinitely many primes greater than 20. Therefore A is an infinite set, not a finite or singleton 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.
