**(i) **Given that,

A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

To find,

A ∩ (B ∪ C)

The intersection of sets A and B is the set of all elements which are common to both A and B.

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13}

= {7, 9, 11} ∪ {11}

= {7, 9, 11}

**(ii)** To find, A ∩ D

The intersection of sets A and B is the set of all elements which are common to both A and B.

A ∩ D = {3, 5, 7, 9, 11} ∩ {15, 17}

A ∩ D = Φ

**(iii) **To find, A ∩ (B ∪ D)

The intersection of sets A and B is the set of all elements which are common to both A and B.

A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D)

A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13}

= {7, 9, 11} ∪ Φ

= {7, 9, 11}

**(iv)** To find, (A ∩ B) ∩ (B ∪ C)

The intersection of sets A and B is the set of all elements which are common to both A and B.

A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13}

A ∩ B = {7, 9, 11}

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

= {7, 9, 11, 13, 15}

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

= {7, 9, 11}

**(v)** To find,(A ∪ D) ∩ (B ∪ C)

The intersection of sets A and B is the set of all elements which are common to both A and B.

A ∩ D = {3, 5, 7, 9, 11} ∩ {15, 17}

A ∩ D = {3, 5, 7, 9, 11, 15, 17)

B ∪ C = {7, 9, 11, 13} ∪ {11, 13, 15}

= {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}

Answered by Pragya Singh | 11 months agoFind the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.