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Ex 1.5, 4 - If U = {1, 2, 3, 4, 5 ,6, 7, 8, 9}. Verify (i) (A U B)' =

Ex 1.5, 4 - Chapter 1 Class 11 Sets - Part 2

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Ex 1.5, 4 - Chapter 1 Class 11 Sets - Part 3 Ex 1.5, 4 - Chapter 1 Class 11 Sets - Part 4

 

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Ex 1.5, 4 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} , A = {2, 4, 6, 8} and B = {2, 3, 5, 7} , verify that (i) (A ∪ B)’ = A’∩ B’ A ∪ B = {2, 4, 6, 8} ∪ {2, 3, 5, 7} = {2, 3, 4, 5, 6, 7, 8} (A ∪ B)’ = U – (A ∪ B) = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 3, 4, 5, 6, 7, 8} = {1, 9} A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8} = {1, 3, 5, 7, 9} B’ = U – B = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 3, 5, 7} = {1, 4, 6, 8, 9} A’ ∩ B’ = {1, 3, 5, 7, 9} ∩ {1, 4, 6, 8, 9} = {1, 9} ∩ Intersection – Common of two sets ∪ Union - Combination of two sets Thus, (A ∪ B)’ = A’ ∩ B’ Hence Verified Ex 1.5, 4 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} , A = {2, 4, 6, 8} and B = {2, 3, 5, 7} , verify that (ii) (A ∩ B)’ = A’ ∪ B’ A ∩ B = {2, 4, 6, 8} ∩ {2, 3, 5, 7} = {2} (A ∩ B)’ = U – (A ∩ B) = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2} = {1, 3, 4, 5, 6, 7, 8, 9} ∩ Intersection – Common of two sets ∪ Union - Combination of two sets A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8} = {1, 3, 5, 7, 9} B’ = U – B = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 3, 5, 7} = {1, 4, 6, 8, 9} A’ ∪ B’ = {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9} Thus, (A ∩ B)’ = A’ ∪ B’ Hence Veraified

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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.