If U = {1, 2, …, 144} and A = {x : x is not divisible by 12}, what is |A′|?
Answer and explanation
Correct answer: 12
A consists of the numbers in U that are not divisible by 12. Therefore, its complement A′ consists exactly of the numbers in U that are divisible by 12. The positive multiples of 12 not exceeding 144 are 12, 24, 36, …, 144. Their number is 144 ÷ 12 = 12, because the kth multiple is 12k and 12k ≤ 144 gives k ≤ 12. Hence |A′| = 12, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
A consists of the numbers in U that are not divisible by 12. Therefore, its complement A′ consists exactly of the numbers in U that are divisible by 12. The positive multiples of 12 not exceeding 144 are 12, 24, 36, …, 144. Their number is 144 ÷ 12 = 12, because the kth multiple is 12k and 12k ≤ 144 gives k ≤ 12. Hence |A′| = 12, so option C 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.
