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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

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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 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,... } .

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