Sets Operations
If A and B are two sets such that A ⊂ B, which of the following is always true?
Select the correct option:
Solution
All of the above
The condition A⊂B (A is a subset of B) means every element in A is already in B.
- Intersection: Since everything in A is in B, the shared elements are exactly the set A. Thus A∩B=A is true.
- Union: Adding elements of A to B adds nothing new, so the result is just set B. Thus A∪B=B is true.
- Difference: A−B removes from A all elements that are also in B. Since all elements of A are in B, nothing remains. Thus A−B=∅ is true.
- Conclusion: All listed statements are fundamental consequences of the subset relation.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
All of the above
The condition A⊂B (A is a subset of B) means every element in A is already in B.
- Intersection: Since everything in A is in B, the shared elements are exactly the set A. Thus A∩B=A is true.
- Union: Adding elements of A to B adds nothing new, so the result is just set B. Thus A∪B=B is true.
- Difference: A−B removes from A all elements that are also in B. Since all elements of A are in B, nothing remains. Thus A−B=∅ is true.
- Conclusion: All listed statements are fundamental consequences of the subset relation.
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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