If U = {1, 2, ..., 20} and A = {x : x is divisible by 3}, how many elements are in A'?
Answer and explanation
Correct answer: 14
The complement A' consists of elements in U that are not in A. The multiples of 3 from 1 to 20 are 3, 6, 9, 12, 15 and 18, so |A| = 6. Since U has 20 elements, the complement-count rule gives |A'| = |U| − |A| = 20 − 6 = 14. Hence option B is correct. The other numerical choices result from miscounting the multiples or subtracting incorrectly.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The complement A' consists of elements in U that are not in A. The multiples of 3 from 1 to 20 are 3, 6, 9, 12, 15 and 18, so |A| = 6. Since U has 20 elements, the complement-count rule gives |A'| = |U| − |A| = 20 − 6 = 14. Hence option B is correct. The other numerical choices result from miscounting the multiples or subtracting incorrectly.
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.
