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 :
(i) A∩B (ii) A∩C (iii) A∩D
(iv) B∩C (v) B∩D (vi) C∩D
Here A = {x : x is a natural number}
= {1, 2, 3, 4, 5, ............}
B = {x : x is an even natural number}
= {2, 4, 6, .............}
C = {x : x is a an odd natural number}
= {1, 3, 5, 7, ............}
and D = {x : x is a prime number}
= {2, 3, 5, 7, ............}
(i) A∩B = {x : x is a natural number} ∩ {x : x is an even natural number}
= {x : x is an even natural number}
= B
(ii) A∩C = {x : x is a natural number} ∩ {x : x is an odd natural number}
= {x : x is an odd natural number}
= C
(iii) A∩D = {x : x is a natural number} ∩ {x : x is a prime number}
= {x : x is a prime number}
= D
(iv) B∩C = {x : x is an even natural number} ∩ {x : x is an odd natural number}
= Φ
(v) B∩D = {x : x is an even natural number} ∩ {x : x is a prime number}
= {2}
(vi) C∩D = {x : x is an odd natural number} ∩ {x : x is a prime number}
= {x : x is an odd prime number} = D -{2}