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Using the property of sets prove that A intersection (A union B) is equal to A?
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Using the property of sets prove that A intersection (A union B) is eq...
Proof that A ∩ (A ∪ B) = A:
1. Definition of Intersection and Union:
- Intersection (A ∩ B) of two sets A and B contains all elements that are in both sets.
- Union (A ∪ B) of two sets A and B contains all elements that are in either set.
2. Property of Union:
- A ∪ B includes all elements in set A and all elements in set B.
3. Property of Intersection:
- A ∩ (A ∪ B) will include only the elements that are common to both A and (A ∪ B).
4. Explanation of A ∩ (A ∪ B):
- A ∪ B includes all elements in A, so A ∩ (A ∪ B) will include all elements that are in both A and (A ∪ B).
- Since A is already a subset of (A ∪ B), the intersection of A and (A ∪ B) will only include elements that are in A.
5. Conclusion:
- Since A ∩ (A ∪ B) includes only elements that are in both A and (A ∪ B), and (A ∪ B) includes all elements in A, the intersection A ∩ (A ∪ B) will be equal to A.
Therefore, by using the property of sets, we have proven that A ∩ (A ∪ B) is equal to A.
1. Definition of Intersection and Union:
- Intersection (A ∩ B) of two sets A and B contains all elements that are in both sets.
- Union (A ∪ B) of two sets A and B contains all elements that are in either set.
2. Property of Union:
- A ∪ B includes all elements in set A and all elements in set B.
3. Property of Intersection:
- A ∩ (A ∪ B) will include only the elements that are common to both A and (A ∪ B).
4. Explanation of A ∩ (A ∪ B):
- A ∪ B includes all elements in A, so A ∩ (A ∪ B) will include all elements that are in both A and (A ∪ B).
- Since A is already a subset of (A ∪ B), the intersection of A and (A ∪ B) will only include elements that are in A.
5. Conclusion:
- Since A ∩ (A ∪ B) includes only elements that are in both A and (A ∪ B), and (A ∪ B) includes all elements in A, the intersection A ∩ (A ∪ B) will be equal to A.
Therefore, by using the property of sets, we have proven that A ∩ (A ∪ B) is equal to A.
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Using the property of sets prove that A intersection (A union B) is equal to A?
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Using the property of sets prove that A intersection (A union B) is equal to A? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Using the property of sets prove that A intersection (A union B) is equal to A? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using the property of sets prove that A intersection (A union B) is equal to A?.
Using the property of sets prove that A intersection (A union B) is equal to A? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Using the property of sets prove that A intersection (A union B) is equal to A? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using the property of sets prove that A intersection (A union B) is equal to A?.
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