If A = {x ∈ ℕ : x is prime, x is even, and x < 10}, then A is equal to:
Answer and explanation
Correct answer: {2}
The natural numbers less than 10 that are even are 2, 4, 6, and 8. Among these numbers, only 2 is prime, because a prime number has exactly two distinct positive divisors, 1 and itself. Therefore, the conditions “even,” “prime,” and “less than 10” are satisfied simultaneously only by 2. Hence A is the singleton set {2}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
{2}
Why is this the correct answer?
The natural numbers less than 10 that are even are 2, 4, 6, and 8. Among these numbers, only 2 is prime, because a prime number has exactly two distinct positive divisors, 1 and itself. Therefore, the conditions “even,” “prime,” and “less than 10” are satisfied simultaneously only by 2. Hence A is the singleton set {2}, making option A 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.
