In a universal set \(U\) of 120 students, 70 study mathematics, 65 study physics, and 30 study both. How many study neither mathematics nor physics?
Advertisement
Answer and explanation
Correct answer: 15
Let the mathematics and physics sets be M and P. By inclusion-exclusion, \(|M\cup P|=|M|+|P|-|M\cap P|=70+65-30=105\). Students studying neither subject lie outside this union, so their number is \(|U|-|M\cup P|=120-105=15\). Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
Let the mathematics and physics sets be M and P. By inclusion-exclusion, \(|M\cup P|=|M|+|P|-|M\cap P|=70+65-30=105\). Students studying neither subject lie outside this union, so their number is \(|U|-|M\cup P|=120-105=15\). Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
Advertisement