Question

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 1

(i) A ∩ B = {7, 9, 11}
(ii) B ∩ C = {11, 13} 

(iii) A ∩ C ∩ D = { A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ 

(iv) A ∩ C = {11} (v) B ∩ D = Φ 

(vi) A ∩ (B C) = (A ∩ B) (A ∩ C) = {7, 9, 11} {11} = {7, 9, 11} 

(vii) A ∩ D = Φ 

(viii) A ∩ (B D) = (A ∩ B) (A ∩ D) = {7, 9, 11} Φ = {7, 9, 11} 

(ix) (A ∩ B) ∩ (B C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11} 

(x) (A D) ∩ (B C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15}