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

Asked by Abhisek | 11 months ago |  59

1 Answer

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

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}

 

(ii) To find B ∩ C

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

B ∩ C = {7, 9, 11, 13} ∩ {11, 13, 15}

= B ∩ C = {11, 13}

 

(iii) To find, A ∩ C ∩ D

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

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

{11} ∩ {15, 17} = Φ

 

(iv) To find, A ∩ C

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

A ∩ C = {3, 5, 7, 9, 11} ∩ {11, 13, 15}

A ∩ C = {11}

 

(v) To find, B ∩ D

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

B ∩ D = {7, 9, 11, 13} ∩ {15, 17}

B ∩ D = Φ

Answered by Pragya Singh | 11 months ago

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