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Example 22 - Let A = {2, 3} and B = {3, 4, 5}. Find A', B' - Examples

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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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 } 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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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