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 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}.