If U = {1, 2, ..., 81}, A = {x : x ∈ U, 3 divides x}, and B = {x : x ∈ U, 27 divides x}, how many elements are in B' ∩ A?
Answer and explanation
Correct answer: 24
The set A contains all multiples of 3 from 1 to 81, so n(A) = 81 ÷ 3 = 27. The set B contains the multiples of 27: 27, 54, and 81, so n(B) = 81 ÷ 27 = 3. Since every multiple of 27 is also a multiple of 3, B is a subset of A. Therefore B' ∩ A consists of the elements of A not in B, and its cardinality is 27 − 3 = 24.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The set A contains all multiples of 3 from 1 to 81, so n(A) = 81 ÷ 3 = 27. The set B contains the multiples of 27: 27, 54, and 81, so n(B) = 81 ÷ 27 = 3. Since every multiple of 27 is also a multiple of 3, B is a subset of A. Therefore B' ∩ A consists of the elements of A not in B, and its cardinality is 27 − 3 = 24.
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.
