Among 65 people, 31 like cricket, 29 like football, and 11 like both. How many like neither sport?
Answer and explanation
Correct answer: 16
First find the number who like at least one sport using inclusion–exclusion: \(n(C\cup F)=n(C)+n(F)-n(C\cap F)=31+29-11=49\). The people who like neither sport are outside this union. Hence, neither \(=65-49=16\). Therefore, option A is correct. Subtracting the overlap once prevents double-counting those who like both sports.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
First find the number who like at least one sport using inclusion–exclusion: \(n(C\cup F)=n(C)+n(F)-n(C\cap F)=31+29-11=49\). The people who like neither sport are outside this union. Hence, neither \(=65-49=16\). Therefore, option A is correct. Subtracting the overlap once prevents double-counting those who like both sports.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
