In a class, 28 students study Hindi, 22 study English, and 10 study both. How many students study Hindi or English?
Answer and explanation
Correct answer: 40
Let H be the set of students studying Hindi and E be the set studying English. The phrase “Hindi or English” means the union H ∪ E, including students who study both subjects. Therefore, n(H ∪ E) = n(H) + n(E) − n(H ∩ E) = 28 + 22 − 10 = 40. The subtraction prevents the ten students studying both subjects from being counted twice.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
Let H be the set of students studying Hindi and E be the set studying English. The phrase “Hindi or English” means the union H ∪ E, including students who study both subjects. Therefore, n(H ∪ E) = n(H) + n(E) − n(H ∩ E) = 28 + 22 − 10 = 40. The subtraction prevents the ten students studying both subjects from being counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
