If U = {1, 2, ..., 54}, A = {x : x ∈ U and 6 divides x}, and B = {x : x ∈ U and 9 divides x}, what is n(A′ ∩ B)?
Answer and explanation
Correct answer: 3 (तीन)
The set B contains the multiples of 9 from 1 to 54: B = {9, 18, 27, 36, 45, 54}. The complement A′ contains all elements of U that are not divisible by 6. Among the elements of B, 18, 36, and 54 are divisible by 6, so they are excluded from A′. The remaining elements are 9, 27, and 45. Therefore, A′ ∩ B = {9, 27, 45}, and its cardinality is n(A′ ∩ B) = 3.
Frequently asked questions
What is the correct answer to this question?
3 (तीन)
Why is this the correct answer?
The set B contains the multiples of 9 from 1 to 54: B = {9, 18, 27, 36, 45, 54}. The complement A′ contains all elements of U that are not divisible by 6. Among the elements of B, 18, 36, and 54 are divisible by 6, so they are excluded from A′. The remaining elements are 9, 27, and 45. Therefore, A′ ∩ B = {9, 27, 45}, and its cardinality is n(A′ ∩ B) = 3.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
