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If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number} Find A ∩ B, A ∩ C, A ∩ D, B ∩ C, B ∩ D, C ∩ D.

Answer»

Given sets are 

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ……} 

B = {2, 4, 6, 8, 10, …….} 

C = {1, 3, 5, 7, 9, …….} 

D = {2, 3, 5, 7, 11, …….} 

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

= {2, 4, 6, 8, 10, ……} 

A ∩ C = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, …} ∩ {1, 3, 5, 7, 9 } 

= {1, 3, 5, 7, 9, ……} 

A ∩ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …} ∩ {2, 3, -5, 7, 11,….} 

= {2, 3, 5, 7, 11, ……} 

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

 { } = φ 

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

= {2} 

C ∩ D = {1, 3, 5, 7, 9, ……} ∩ {2, 3, 5, 7, 11, 13, ……} 

= {3, 5, 7, …..}



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