Sets Operations
In a survey of 100 people, 60 like tea, 50 like coffee, 30 like juice, 20 like tea and coffee, 15 like coffee and juice, 10 like tea and juice, and 5 like all three. How many people like exactly one beverage?
Select the correct option:
Solution
65
- Exclusive Count Formula: n(Exactly 1)=∑n(A)−2∑n(A∩B)+3n(A∩B∩C).
- Calculate Grouped Values:
- Sum individual: 60+50+30=140.
- Sum overlaps (double): 20+15+10=45.
- Triple overlap: 5.
- Apply Formula:
- Exactly1=140−2(45)+3(5)
- Exactly1=140−90+15=65.
- Result: 65 people.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
65
- Exclusive Count Formula: n(Exactly 1)=∑n(A)−2∑n(A∩B)+3n(A∩B∩C).
- Calculate Grouped Values:
- Sum individual: 60+50+30=140.
- Sum overlaps (double): 20+15+10=45.
- Triple overlap: 5.
- Apply Formula:
- Exactly1=140−2(45)+3(5)
- Exactly1=140−90+15=65.
- Result: 65 people.
This hard 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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