(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}