In a group, 24 students study Hindi, 18 study English, and 7 study both languages. How many students study only Hindi?
Answer and explanation
Correct answer: 17
Let H be the set of students studying Hindi and E the set studying English. Students counted in H ∩ E study both languages, so they must be removed from the total Hindi group to find only Hindi: n(H − E) = n(H) − n(H ∩ E) = 24 − 7 = 17. Therefore, 17 students study only Hindi. The value 11 is the number studying only English, 7 is the number studying both, and 35 is an incorrect addition that double-counts the overlap.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
Let H be the set of students studying Hindi and E the set studying English. Students counted in H ∩ E study both languages, so they must be removed from the total Hindi group to find only Hindi: n(H − E) = n(H) − n(H ∩ E) = 24 − 7 = 17. Therefore, 17 students study only Hindi. The value 11 is the number studying only English, 7 is the number studying both, and 35 is an incorrect addition that double-counts the overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
