If A = {x : x ϵ N}, B = {x : x ϵ N and x is even), C = {x : x ϵ N and x is odd} and D = {x : x ϵ N and x is prime} then find:
(i) A ∩ B
(ii) A ∩ C
(iii) A ∩ D
(iv) B ∩ C
(v) B ∩ D
(vi) C ∩ D
Given; A = {x : x ϵ N}, B = {x : x ϵ N and x is even), C = {x : x ϵ N and x is odd} and D = {x : x ϵ N and x is prime}
(i) A ∩ B = {x : x ϵ N and x is even}
(ii) A ∩ C = {x : x ϵ N and x is odd}
(iii) A ∩ D = {x : x ϵ N and x is prime}
(iv) B ∩ C = Φ or {}
(v) B ∩ D = {2} [∵ 2 is the only even prime number]
(vi) C ∩ D = {x : x ϵ N and x is prime and x ≠ 2}