If U = {1, 2, ..., 40}, 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 is divisible by 2 and therefore has at least two factors, so it is not prime. The number 2 itself has exactly two positive factors, 1 and 2, and is the only even prime. Hence A ∩ B = {2}.
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 is divisible by 2 and therefore has at least two factors, so it is not prime. The number 2 itself has exactly two positive factors, 1 and 2, and is the only even prime. Hence A ∩ B = {2}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
