Question

7.If A= {x : x is a natural number }, B = {x : x is an even natural number)C= {x:x is an odd natural number) andD = {x : x is a prime number ], find) An B(iv) BC(ii) AnID(vi) Cn Di) AnC

Answer 1

Given, A={ 1,2,3,4,5,... } , B={ 2,4,6,8,10,... } , C={ 1,3,5,7,9,... } and D={ 2,3,5,7,11,... } .

(i)

The intersection between sets A and B is denoted as A∩B .

So, the intersection between sets A and B is

A∩B={ 1,2,3,4,5,... }∩{ 2,4,6,8,10,... } ={ 2,4,6,8,10... }

Hence, A∩B={ 2,4,6,8,10,... } .

(ii)

The intersection of the sets A and C is denoted as A∩C .

Given, A={ 1,2,3,4,5,... } and C={ 1,3,5,7,9,... }

So, A∩C can be calculated as

A∩C={ 1,2,3,4,5,... }∩{ 1,3,5,7,9,... } ={ 1,3,5,7,9,... }

Hence, A∩C={ 1,3,5,7,9,... } .

(iii)

The intersection of the sets A and D is denoted as A∩D .

Given, A={ 1,2,3,4,5,... } and D={ 2,3,5,7,11,... } .

So, A∩D can be calculated as

A∩D={ 1,2,3,4,5,... }∩{ 2,3,5,7,11,... } ={ 2 }

Hence, A∩D={ 2 } .

(iv)

The intersection of the sets B and C is denoted as B∩C .

Given, B={ 2,4,6,8,10,... } and C={ 1,3,5,7,9,... } .

So, the intersection between B and C is

B∩C={ 2,4,6,8,10,... }∩{ 1,3,5,7,9,... } =ϕ

Hence, B∩C=ϕ .

(v)

The intersection of the sets B and D is denoted as B∩D .

Given, B={ 2,4,6,8,10,... } and D={ 2,3,5,7,11,... } .

So, the intersection between sets B and D is

B∩D={ 2,4,6,8,10... }∩{ 2,3,5,7,11,... } ={ 2 }

Hence, B∩D={ 2 } .

(vi)

The intersection of the sets C and D is denoted as C∩D .

Given, C={ 1,3,5,7,9,... } and D={ 2,3,5,7,11,... } .

So, the intersection between C and D is

C∩D={ 1,3,5,7,9,... }∩{ 2,3,5,7,11,... } ={ 3,5,7,11,13,17,19,... }

Hence, C∩D={ 3,5,7,11,13,17,19,... } .