In a group of 150 students, 82 study mathematics, 74 study biology, and 36 study both subjects. How many study neither subject?
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Answer and explanation
Correct answer: 30
Let \(M\) be the set of students studying mathematics and \(B\) the set studying biology. By inclusion–exclusion, \(n(M\cup B)=n(M)+n(B)-n(M\cap B)=82+74-36=120\). The students studying neither subject are outside this union, so their number is \(150-120=30\).
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
Let \(M\) be the set of students studying mathematics and \(B\) the set studying biology. By inclusion–exclusion, \(n(M\cup B)=n(M)+n(B)-n(M\cap B)=82+74-36=120\). The students studying neither subject are outside this union, so their number is \(150-120=30\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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