find (i) A ∩ B (ii) B ∩ C (iii) A ∩ C ∩ D (iv) A ∩ C (v) B ∩ D (vi) A ∩ (B ∪ C) (vii) A ∩ D (viii) A ∩ (B ∪ D) (ix) (A ∩ B) ∩ (B ∪ C) (x) (A ∪ D) ∩ (B ∪ C)

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; 
find
(i) A ∩ B
(ii) B ∩ C
(iii) A ∩ C ∩ D
(iv) A ∩ C
(v) B ∩ D
(vi) A ∩ (B ∪ C)
(vii) A ∩ D
(viii) A ∩ (B ∪ D)
(ix) (A ∩ B) ∩ (B ∪ C)
(x) (A ∪ D) ∩ (B ∪ C)
Answer
(i) A ∩ B = {7, 9, 11}
(ii) B ∩ C = {11, 13}
(iii) A ∩ C ∩ D = ( A ∩ C) ∩ D
A ∩ C = {11} and D = {15, 17}
Plug the values we get.
( A ∩ C) ∩ D = {11} ∩ {15, 17} = Φ
(iv) A ∩ C = {11}
(v) B ∩ D = Φ
(vi) A ∩ (B ∪ C)
A= {3, 5, 7, 9, 11}
(B ∪ C) ={7, 9, 11, 13} ∪ {11, 13, 15} = {7, 9, 11, 13, 15}
A ∩ (B ∪ C) = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
(vii) A ∩ D ={ } = Φ
(viii) A= {3, 5, 7, 9, 11}
(B ∪ D) ={7, 9, 11, 13} ∪ {15, 17} = {7, 9, 11, 13, 15, 17}
A ∩ (B ∪ D) {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15, 17}= {7, 9, 11}
(ix) (A ∩ B) = {7, 9, 11} and (B ∪ C)= {7, 9, 11, 13, 15}
(A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
(x) (A ∪ D) = {3, 5, 7, 9, 11, 15, 17) and (B ∪ C) = {7, 9, 11, 13, 15}
(A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15}