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 | 1 year ago |  71

##### 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 | 1 year ago

### Related Questions

#### If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

#### Prove that A – B = A ∩ B.’

Prove that A – B = A ∩ B.’

#### Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.