In a class, 40 students study mathematics, 34 study science, and 18 study both. How many study only mathematics?
Answer and explanation
Correct answer: 22
The number studying only mathematics is found by removing the students who study both subjects from the total mathematics group. Thus only mathematics = n(M) − n(M ∩ S) = 40 − 18 = 22. Option B, 16, is the number studying only science; option C is the union, and option D double-counts the overlap. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The number studying only mathematics is found by removing the students who study both subjects from the total mathematics group. Thus only mathematics = n(M) − n(M ∩ S) = 40 − 18 = 22. Option B, 16, is the number studying only science; option C is the union, and option D double-counts the overlap. Therefore 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).
