Sets Operations
In a class of 50 students, 30 like Mathematics, 25 like Physics, and 10 like both subjects. How many students like neither Mathematics nor Physics?
Select the correct option:
Solution
5
- Identify Sets: Let M be the set of Math lovers and P be Physics lovers.
- Find Union (Liking at least one): n(M∪P)=n(M)+n(P)−n(M∩P).
- n(M∪P)=30+25−10=45.
- Find Complement (Liking neither): Total students minus the union.
- Neither=n(U)−n(M∪P)
- Neither=50−45=5.
- Result: 5 students like neither subject.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
5
- Identify Sets: Let M be the set of Math lovers and P be Physics lovers.
- Find Union (Liking at least one): n(M∪P)=n(M)+n(P)−n(M∩P).
- n(M∪P)=30+25−10=45.
- Find Complement (Liking neither): Total students minus the union.
- Neither=n(U)−n(M∪P)
- Neither=50−45=5.
- Result: 5 students like neither subject.
This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of sets operations. It appeared in the 2025 exam.
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