If U has 120 students, 72 study Hindi and 55 study English, while 30 study both, how many students study neither Hindi nor English?
Answer and explanation
Correct answer: 23
Let H be the set of students studying Hindi and E be the set studying English. By the inclusion–exclusion principle, n(H ∪ E) = n(H) + n(E) − n(H ∩ E) = 72 + 55 − 30 = 97. Students studying neither subject belong to the complement of H ∪ E. Therefore, their number is n(U) − n(H ∪ E) = 120 − 97 = 23. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Let H be the set of students studying Hindi and E be the set studying English. By the inclusion–exclusion principle, n(H ∪ E) = n(H) + n(E) − n(H ∩ E) = 72 + 55 − 30 = 97. Students studying neither subject belong to the complement of H ∪ E. Therefore, their number is n(U) − n(H ∪ E) = 120 − 97 = 23. Hence, 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.
