In a class, 30 students study Mathematics, 22 students study Physics, and 12 students study both subjects. How many students study at least one subject?
Answer and explanation
Correct answer: 40
“At least one subject” means the union of the Mathematics and Physics sets. By the inclusion–exclusion principle, n(M ∪ P) = n(M) + n(P) − n(M ∩ P). Therefore, n(M ∪ P) = 30 + 22 − 12 = 40. We subtract the 12 students studying both subjects because they were counted twice in 30 + 22. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
“At least one subject” means the union of the Mathematics and Physics sets. By the inclusion–exclusion principle, n(M ∪ P) = n(M) + n(P) − n(M ∩ P). Therefore, n(M ∪ P) = 30 + 22 − 12 = 40. We subtract the 12 students studying both subjects because they were counted twice in 30 + 22. Thus, option A 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).
