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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)’

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(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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