If A = {x ∈ ℕ : x is prime and even}, what type of set is A?
Answer and explanation
Correct answer: {2}, a singleton finite set
A prime number has exactly two positive divisors, while an even number is divisible by 2. The only number that is both prime and even is 2; every other even number has at least 2 and another divisor, so it is composite. Therefore A = {2}. This set has one element and is a singleton finite set, making option B correct.
Frequently asked questions
What is the correct answer to this question?
{2}, a singleton finite set
Why is this the correct answer?
A prime number has exactly two positive divisors, while an even number is divisible by 2. The only number that is both prime and even is 2; every other even number has at least 2 and another divisor, so it is composite. Therefore A = {2}. This set has one element and is a singleton finite set, making option B correct.
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.
