Example 25 - Chapter 1 Class 11 Sets
Last updated at Dec. 13, 2024 by Teachoo
Last updated at Dec. 13, 2024 by Teachoo
Example 25 Show that A ∪ B = A ∩ B implies A = B In order to prove A = B, we should prove A is a subset of B i.e. A ⊂ B & B is a subset of A i.e. B ⊂ A Let x ∈ A. Then, x ∈ A ∪ B. Since A ∪ B = A ∩ B , ∴ x ∈ A ∩ B. So, x ∈ B. ∴ If x ∈ A , then x ∈ B i.e. if an elements belongs to set A, then it must belong to set B also Therefore, A ⊂ B. Similarly, if y ∈ B, then y ∈ A ∪ B. Since A ∪ B = A ∩ B, y ∈ A ∩ B. So, y ∈ A. ∴ If y ∈ B , then y ∈ A i.e. if an elements belongs to set B, then it must belong to set A also Therefore, B ⊂ A. From (1) & (2) A ⊂ B & B ⊂ A Thus, A = B Hence shown
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Example 25 You are here
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About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo