Sets Operations
If n(A) = 15, n(B) = 20, and n(A ∪ B) = 30, what is the value of n(A ∩ B)?
Select the correct option:
Solution
5
- Principle of Inclusion-Exclusion: For any two finite sets, the formula is n(A∪B)=n(A)+n(B)−n(A∩B).
- Insert Values:
- 30=15+20−n(A∩B)
- Algebraic Solution:
- 30=35−n(A∩B)
- n(A∩B)=35−30=5.
- Result: The number of common elements is 5.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
5
- Principle of Inclusion-Exclusion: For any two finite sets, the formula is n(A∪B)=n(A)+n(B)−n(A∩B).
- Insert Values:
- 30=15+20−n(A∩B)
- Algebraic Solution:
- 30=35−n(A∩B)
- n(A∩B)=35−30=5.
- Result: The number of common elements is 5.
This easy 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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