CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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

Open in App
Solution

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 AB .

So, the intersection between sets A and B is

AB={ 1,2,3,4,5,... }{ 2,4,6,8,10,... } ={ 2,4,6,8,10... }

Hence, AB={ 2,4,6,8,10,... } .

(ii)

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

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

So, AC can be calculated as

AC={ 1,2,3,4,5,... }{ 1,3,5,7,9,... } ={ 1,3,5,7,9,... }

Hence, AC={ 1,3,5,7,9,... } .

(iii)

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

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

So, AD can be calculated as

AD={ 1,2,3,4,5,... }{ 2,3,5,7,11,... } ={ 2 }

Hence, AD={ 2 } .

(iv)

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

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

So, the intersection between B and C is

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

Hence, BC=ϕ .

(v)

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

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

So, the intersection between sets B and D is

BD={ 2,4,6,8,10... }{ 2,3,5,7,11,... } ={ 2 }

Hence, BD={ 2 } .

(vi)

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

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

So, the intersection between C and D is

CD={ 1,3,5,7,9,... }{ 2,3,5,7,11,... } ={ 3,5,7,11,13,17,19,... }

Hence, CD={ 3,5,7,11,13,17,19,... } .


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Where Friction?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon