If U = {1, 2, ..., 36}, A is the set of square numbers and B is the set of multiples of 3, what is n(A ∩ B)?
Answer and explanation
Correct answer: 2
The intersection requires numbers that are both perfect squares and multiples of 3. The square numbers from 1 through 36 are 1, 4, 9, 16, 25, and 36. Checking divisibility by 3 leaves 9 and 36 only; the other squares are not multiples of 3. Hence A ∩ B = {9,36}, which has cardinality 2. Therefore option A is correct; counting every square or every multiple of 3 would answer a different question.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The intersection requires numbers that are both perfect squares and multiples of 3. The square numbers from 1 through 36 are 1, 4, 9, 16, 25, and 36. Checking divisibility by 3 leaves 9 and 36 only; the other squares are not multiples of 3. Hence A ∩ B = {9,36}, which has cardinality 2. Therefore option A is correct; counting every square or every multiple of 3 would answer a different question.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
