Sets Operations
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, find n(A' ∩ B').
Select the correct option:
Solution
4
- Method 1 (De Morgan's Law): A′∩B′=(A∪B)′. This is often faster.
- Find Union: A∪B={1,2,3,4,5,6}.
- Find Complement: (A∪B)′ consists of elements in U but not in the union.
- (A∪B)′={7,8,9,10}.
- Method 2 (Elemental):
- A′={5,6,7,8,9,10}
- B′={1,2,7,8,9,10}
- Intersection: {7,8,9,10}.
- Count: There are 4 elements.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
4
- Method 1 (De Morgan's Law): A′∩B′=(A∪B)′. This is often faster.
- Find Union: A∪B={1,2,3,4,5,6}.
- Find Complement: (A∪B)′ consists of elements in U but not in the union.
- (A∪B)′={7,8,9,10}.
- Method 2 (Elemental):
- A′={5,6,7,8,9,10}
- B′={1,2,7,8,9,10}
- Intersection: {7,8,9,10}.
- Count: There are 4 elements.
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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