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 

(vii) 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 = φ 

(iv) A∩C ={11} 

(v) B∩D ={ } =φ 

(vi ) A ∩ {B ∪ C) = {3, 5, 7,9,11}∩{7,9,11,13,15}={7,9,11} A∩D = φ 

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

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

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

= {7,9,11,15}