If U = {1, 2, ..., 50}, A is the set of prime numbers and B is the set of multiples of 5, what is A ∩ B?
Answer and explanation
Correct answer: {5}
To belong to A ∩ B, a number must satisfy both conditions: it must be prime and also a multiple of 5. The only prime multiple of 5 is 5 itself, because every other positive multiple of 5 is divisible by 5 and has at least one additional factor. Therefore A ∩ B = {5}. The universal set ending at 50 does not change this conclusion.
Frequently asked questions
What is the correct answer to this question?
{5}
Why is this the correct answer?
To belong to A ∩ B, a number must satisfy both conditions: it must be prime and also a multiple of 5. The only prime multiple of 5 is 5 itself, because every other positive multiple of 5 is divisible by 5 and has at least one additional factor. Therefore A ∩ B = {5}. The universal set ending at 50 does not change this conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
