If U = {1, 2, 3, ..., 64}, A is the set of square numbers in U, and B is the set of even numbers in U, then what is n(A ∩ B)?
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Answer and explanation
Correct answer: 4
The intersection A ∩ B contains numbers that are both perfect squares and even. The square numbers from 1 to 64 are 1, 4, 9, 16, 25, 36, 49, and 64. The even members are 4, 16, 36, and 64. Thus A ∩ B = {4, 16, 36, 64}, which has four elements, so n(A ∩ B) = 4. The other options do not count this set correctly.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The intersection A ∩ B contains numbers that are both perfect squares and even. The square numbers from 1 to 64 are 1, 4, 9, 16, 25, 36, 49, and 64. The even members are 4, 16, 36, and 64. Thus A ∩ B = {4, 16, 36, 64}, which has four elements, so n(A ∩ B) = 4. The other options do not count this set correctly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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