If A = {x ∈ N : x ≤ 40 and x is a perfect square} and B = {x ∈ N : x ≤ 40 and x is even}, where N denotes the positive natural numbers, what is A ∩ B?
Answer and explanation
Correct answer: {4, 16, 36}
The positive perfect squares not exceeding 40 are 1, 4, 9, 16, 25, and 36. Among these, the even numbers are 4, 16, and 36. The intersection requires both conditions simultaneously: being a perfect square and being even. Therefore A ∩ B = {4, 16, 36}. Option C contains odd squares as well and is therefore only A, not the intersection.
Frequently asked questions
What is the correct answer to this question?
{4, 16, 36}
Why is this the correct answer?
The positive perfect squares not exceeding 40 are 1, 4, 9, 16, 25, and 36. Among these, the even numbers are 4, 16, and 36. The intersection requires both conditions simultaneously: being a perfect square and being even. Therefore A ∩ B = {4, 16, 36}. Option C contains odd squares as well and is therefore only A, not the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
