Example 22 - Chapter 1 Class 11 Sets
Last updated at Dec. 13, 2024 by Teachoo
Last updated at Dec. 13, 2024 by Teachoo
Example 22 Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}. Find A′, B′ , A′ ∩ B′, A ∪ B and hence show that (A ∪ B)′ = A′ ∩ B′. A′ = U – A = {1, 2, 3, 4, 5, 6} – {2, 3} = {1, 4, 5, 6} B′ = U – B = {1, 2, 3, 4, 5, 6} – {3, 4, 5} = {1, 2, 6} Now, A′ ∩ B′ = {1, 4, 5, 6} ∩ {1, 2, 6} = {1, 6} ∩ Intersection – Common of two sets ∪ Union - Combination of two sets Also, A ∪ B = {2, 3} ∪ {3, 4, 5} = { 2, 3, 4, 5 } Now, we need to prove (A ∪ B)′ = A′ ∩ B′ (A ∪ B)′ = U – (A ∪ B ) = {1, 2, 3, 4, 5, 6} – {2, 3, 4, 5} = {1, 6} Now, A′ ∩ B′ = {1, 6} & (A ∪ B)′ = {1, 6} Thus, (A ∪ B)′ = A′ ∩ B′ Hence proved
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo