Misc 11  - If A U X = B U X for some set X, show A = B - Chapter 1 - Miscellaneous

  1. Chapter 1 Class 11 Sets
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Misc 11 Let A and B be sets. If A X = B X = and A X = B X for some set X, show that A = B. (Hints: A = A (A X), B = B (B X) and use distributive law) Given: Let A and B be two sets such that A X = B X = and A X = B X for some set X. To prove: A = B Proof: Let A = A (A X) A = A (B X) Using distributive law :A (B C)= (A B) (A C) = (A B) (A X) As A X = given = (A B) A = A B Let B = B (B X) B = B (A X) Using distributive law :A (B C)= (A B) (A C) = (B A) (B X) As B X = = (B A) B = B A B = A B From (1) and (2), A = A B & B = A B A = B Hence proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.