In U = {1, 2, 3, ..., 70}, A is the set of prime numbers and B is the set of even numbers. What is A ∩ B?
Answer and explanation
Correct answer: {2}
The intersection A ∩ B contains numbers that satisfy both conditions: they must be prime and even. Every even number greater than 2 has at least the divisors 1, 2, and itself, so it is composite. The number 2 is the only even prime. Therefore A ∩ B = {2}, making option A correct; option C contains many composite even numbers.
Frequently asked questions
What is the correct answer to this question?
{2}
Why is this the correct answer?
The intersection A ∩ B contains numbers that satisfy both conditions: they must be prime and even. Every even number greater than 2 has at least the divisors 1, 2, and itself, so it is composite. The number 2 is the only even prime. Therefore A ∩ B = {2}, making option A correct; option C contains many composite even numbers.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
