Sets Operations
For sets A, B, and C, if A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C), which law does this represent?
Select the correct option:
Solution
Distributive Law
- Definition: Distribution laws describe how one operation interact with another across parentheses.
- Analysis: Here, the 'intersection' operator (∩) is being applied to each set inside the 'union' bracket (∪). This is analogous to x(y+z)=xy+xz in algebra.
- Conclusion: This is the Distributive Law (specifically, intersection distributivity over union).
- Bonus: Union also distributes over intersection: A∪(B∩C)=(A∪B)∩(A∪C).
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
Distributive Law
- Definition: Distribution laws describe how one operation interact with another across parentheses.
- Analysis: Here, the 'intersection' operator (∩) is being applied to each set inside the 'union' bracket (∪). This is analogous to x(y+z)=xy+xz in algebra.
- Conclusion: This is the Distributive Law (specifically, intersection distributivity over union).
- Bonus: Union also distributes over intersection: A∪(B∩C)=(A∪B)∩(A∪C).
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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