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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Misc 7 Using properties of sets show that A ∪ (A ∩ B) = A In order to prove A ∪ (A ∩ B) = A, we should prove A ∪ (A ∩ B) is a subset of A i.e. A ∪ (A ∩ B) ⊂ A & A is a subset of A ∪ (A ∩ B) i.e. A ⊂ A ∪ (A ∩ B) As set is a subset of itself, A ⊂ A Also, A is a subset of A ∩ B , i.e. A ⊂ A ∩ B as all elements of set A are in A ∩ B Now, A ∪ (A ∩ B) Using distributive law :A ∪ (B ∩ C)= (A ∪ B) ∩ (A ∪ C) = (A) ∩ (A U B) = A = R.H.S Thus, A ∪ (A ∩ B) = A Hence proved Misc 7 Using properties of sets show that A ∪ (A ∩ B) = A Solving L.H.S A ∪ (A ∩ B) Using distributive law :A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) = = (A) ∩ (A U B) = A = R.H.S Thus, A ∪ (A ∩ B) = A Hence proved Misc 7 Using properties of sets show that (ii) A ∩ (A ∪ B) = A. Taking L.H.S A ∩ (A ∪ B) Using distributive law :A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) = = (A) U (A ∩ B) = A = R.H.S Thus A ∩ (A ∪ B) = A. Hence proved

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.