In a class of 40 students, 18 are in the mathematics club and 15 are in the science club. If 6 students are in both clubs, how many students are in neither club?
Answer and explanation
Correct answer: 13
Let M be the mathematics-club set and S be the science-club set. By the inclusion–exclusion principle, n(M ∪ S) = n(M) + n(S) − n(M ∩ S) = 18 + 15 − 6 = 27. Thus, 27 students belong to at least one club. The students in neither club are outside this union, so their number is 40 − 27 = 13. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
Let M be the mathematics-club set and S be the science-club set. By the inclusion–exclusion principle, n(M ∪ S) = n(M) + n(S) − n(M ∩ S) = 18 + 15 − 6 = 27. Thus, 27 students belong to at least one club. The students in neither club are outside this union, so their number is 40 − 27 = 13. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
