Example 30 - Chapter 1 Class 11 Sets
Last updated at Dec. 23, 2019 by Teachoo
Transcript
Example 30 Show that A ∪ B = A ∩ B implies A = B Inorder 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
Examples
Example 1
Example 2
Example 3
Example 4
Example 5 Important
Example 6 Important
Example 7
Example 8
Example 9 Important
Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
Example 15
Example 16
Example 17
Example 18 Important
Example 19
Example 20
Example 21
Example 22 Important
Example 23
Example 24 Important
Example 25 Important
Example 26
Example 27 Important
Example 28
Example 29 Important
Example 30 Important You are here
Example 31 Important
Example 32 Important
Example 33 Important
Example 34 Important
Chapter 1 Class 11 Sets
Serial order wise
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.