

InterviewSolution
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If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 4} and C = {4, 6, 8, 10} then find the value of following sets: (i) (A ∪ B) ∩ B (ii) (A ∩ B) ∪ C (iii) A’ ∪ B’ (iv) (A ∪ B)’ |
Answer» (i) (A ∪ B) ∩ B A ∪ B = { 1,2, 3, 4, 5, 6} ∪ {2, 3, 4} = {1, 2, 3, 4, 5, 6} (A ∪ B) ∩ B = {1, 2, 3, 4, 5, 6} ∩ {2, 3, 4} = {2, 3, 4} = B (ii) (A ∩ B) ∪ C A ∩ B = {1, 2, 3, 4, 5, 6} ∩ {2, 3, 4} = {2, 3, 4} (A ∩ B) ∪ C = {2, 3, 4} ∪ {4, 6, 8, 10} = {2, 3, 4, 6, 8, 10} (iii) A’ ∪ B’ A = {1, 2, 3, 4, 5, 6} U = {1,2, 3, 4, 5, 6, 7, 8, 9, 10} A’ = U – A = {1,2,…..10} – {1, 2,… 6} = {7, 8, 9, 10} Similarly, B’ = {1, 5, 6, 7, 8, 9, 10} A’ ∪ B’ = {7, 8, 9, 10} ∪ {1, 5, 6, 7, 8, 9, 10} = {1, 5, 6, 7, 8, 9, 10} (iv) (A ∪ B)’ A ∪ B = { 1, 2, 3, 4, 5, 6} = A ∪ {2, 3, 4} = {1, 2, 3, 4, 5, 6} (A ∪ B)’ = U – (A ∪ B) = {1, 2,… 10} – {1, 2, 3, 4, 5, 6} = {7, 8, 9, 10} |
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