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Prove that A union (A intersection B) is equal to a?
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Prove that A union (A intersection B) is equal to a?
Proof that A union (A intersection B) is equal to A
  • Definition of Union and Intersection:

    • A union B is the set of all elements that are in A, in B, or in both A and B. A intersection B is the set of all elements that are common to both A and B.
  • Proof:

    • To prove that A union (A intersection B) is equal to A, we need to show that every element in A union (A intersection B) is also in A, and vice versa.
  • Every element in A union (A intersection B) is in A:

    • Let x be an arbitrary element in A union (A intersection B). This means that x is in A or x is in (A intersection B).
    If x is in A, then x is obviously in A.
    If x is in (A intersection B), then x is in both A and B. Since x is in A, x is also in A union B. Therefore, x is in A.
    In either case, x is in A. This proves that every element in A union (A intersection B) is in A.
  • Every element in A is in A union (A intersection B):

    • Let x be an arbitrary element in A. Since x is in A, x is in A union B. Additionally, x is in A intersection B because x is in both A and B. Therefore, x is in A union (A intersection B).
    This proves that every element in A is in A union (A intersection B).
  • Conclusion:

    • Since every element in A union (A intersection B) is in A, and every element in A is in A union (A intersection B), we can conclude that A union (A intersection B) is equal to A.
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Prove that A union (A intersection B) is equal to a?
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Prove that A union (A intersection 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 Prove that A union (A intersection B) is equal to a? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that A union (A intersection B) is equal to a?.
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