If U = {1, 2, ..., 42}, A is the set of multiples of 3, and B is the set of multiples of 7, what is n((A − B)′)?
Answer and explanation
Correct answer: 30
The set A contains the multiples of 3 up to 42, so n(A) = 42/3 = 14. The elements removed in A − B are those that are also multiples of 7, namely the common multiples of 3 and 7. These are multiples of lcm(3,7) = 21; there are 42/21 = 2 such elements, 21 and 42. Therefore n(A − B) = 14 − 2 = 12. Since U has 42 elements, n((A − B)′) = 42 − 12 = 30. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
The set A contains the multiples of 3 up to 42, so n(A) = 42/3 = 14. The elements removed in A − B are those that are also multiples of 7, namely the common multiples of 3 and 7. These are multiples of lcm(3,7) = 21; there are 42/21 = 2 such elements, 21 and 42. Therefore n(A − B) = 14 − 2 = 12. Since U has 42 elements, n((A − B)′) = 42 − 12 = 30. 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.
