If U = {1, 2, …, 100} and A = {x ∈ U : 8 divides x}, what is n(A')?
Answer and explanation
Correct answer: 88
The elements of A are the positive multiples of 8 not exceeding 100. Their number is floor(100/8) = 12, since the multiples run from 8 through 96. The universal set U contains 100 elements. The complement A' therefore contains all elements of U that are not divisible by 8, so n(A') = 100 − 12 = 88. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
88
Why is this the correct answer?
The elements of A are the positive multiples of 8 not exceeding 100. Their number is floor(100/8) = 12, since the multiples run from 8 through 96. The universal set U contains 100 elements. The complement A' therefore contains all elements of U that are not divisible by 8, so n(A') = 100 − 12 = 88. Thus, 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.
