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Misc 12 - Find sets A, B and C such that A B, B C and A C

Misc 12 - Chapter 1 Class 11 Sets - Part 2

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Misc 12 Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = ∅. A ∩ B should be non-empty, i.e. there should be some common element between A & B Similarly, B ∩ C should be non-empty, i.e. there should be some common element between B & C A ∩ C should be non-empty, i.e. there should be some common element between A & C Also, given that A ∩ B ∩ C is a null set, i.e. there should be not be any element common between A, B & C Let A = {0, 1}, B = {1, 2}, and C = {2, 0}. Now, A ∩ B = {1}, B ∩ C = {2}, and A ∩ C = {0}. ∴ A ∩ B, B ∩ C, and A ∩ C are non-empty. However, A ∩ B ∩ C = ∅

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.