If O₁ = {x : x ∈ ℕ, x is prime and even}, what type of set is O₁?
Answer and explanation
Correct answer: Singleton set
The only even prime number is 2. Every other even natural number is divisible by 2 and therefore has at least the divisors 1, 2, and itself, so it is not prime. Hence O₁ = {2}. Because this set contains exactly one element, it is a singleton set. It is neither empty nor infinite, and it certainly does not contain three elements.
Frequently asked questions
What is the correct answer to this question?
Singleton set
Why is this the correct answer?
The only even prime number is 2. Every other even natural number is divisible by 2 and therefore has at least the divisors 1, 2, and itself, so it is not prime. Hence O₁ = {2}. Because this set contains exactly one element, it is a singleton set. It is neither empty nor infinite, and it certainly does not contain three elements.
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.
