Sets Operations
For any three sets A, B, and C, A - (B ∪ C) equals
Select the correct option:
Solution
(A - B) ∩ (A - C)
- Linguistic Reasoning: A−(B∪C) means "Elements in A that are NOT in B AND NOT in C."
- Convert to Intersection: A∩(B∪C)′.
- Apply De Morgan's Law: (B∪C)′=B′∩C′.
- Expression becomes A∩B′∩C′.
- Rearrange:
- (A∩B′)∩(A∩C′)
- (A−B)∩(A−C).
- Conclusion: This confirms that removing elements of a union is equivalent to the intersection of the individual differences.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
(A - B) ∩ (A - C)
- Linguistic Reasoning: A−(B∪C) means "Elements in A that are NOT in B AND NOT in C."
- Convert to Intersection: A∩(B∪C)′.
- Apply De Morgan's Law: (B∪C)′=B′∩C′.
- Expression becomes A∩B′∩C′.
- Rearrange:
- (A∩B′)∩(A∩C′)
- (A−B)∩(A−C).
- Conclusion: This confirms that removing elements of a union is equivalent to the intersection of the individual differences.
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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