If U = {1, 2, …, 36}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 3 divides x}, what is n(A' ∩ B)?
Answer and explanation
Correct answer: 6
A' ∩ B consists of numbers that are divisible by 3 but not divisible by 2. From 1 to 36, there are floor(36/3) = 12 multiples of 3. Among them, the even ones are multiples of 6, and there are floor(36/6) = 6 such numbers. Removing these 6 even multiples from the 12 multiples of 3 leaves 12 − 6 = 6 numbers. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A' ∩ B consists of numbers that are divisible by 3 but not divisible by 2. From 1 to 36, there are floor(36/3) = 12 multiples of 3. Among them, the even ones are multiples of 6, and there are floor(36/6) = 6 such numbers. Removing these 6 even multiples from the 12 multiples of 3 leaves 12 − 6 = 6 numbers. Hence, option A is correct.
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.
