Question

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

Answer 1

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}