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

(i) A ∩ (B ∪ C)

(ii) A ∩ D

(iii) A ∩ (B ∪ D)

(iv) (A ∩ B) ∩ (B ∪ C)

(v) (A ∪ D) ∩ (B ∪ C)

Asked by Abhisek | 11 months ago |  87

##### Solution :-

(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 ago

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