**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}

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