Question

Which of the following sets are pairs of disjoint sets? Justify your answer. 

(i) A = {3, 4, 5, 6} and B = {2, 5, 7, 9} 

(ii) C = {1, 2, 3, 4, 5} and D = {6, 7, 9, 11} 

(iii) E = {x : x ϵ N, x is even and x < 8} F = {x : x = 3n, n ϵ N, and x < 4} 

(vi) G = {x : x ϵ N, x is even} and H {x : x ϵ N, x is prime} 

(v) J = {x : x ϵ N, x is even} and K = {x : x ϵ N, x is odd}

Answer 1

Disjoint sets have their intersections as Φ. 

(i) A = {3, 4, 5, 6} and B = {2, 5, 7, 9} Are pairs of disjoint sets. 

(ii) C = {1, 2, 3, 4, 5} and D = {6, 7, 9, 11} Are pairs of disjoint sets. 

(iii) E = {x : x ϵ N, x is even and x < 8} = {2, 4, 6} and 

F = {x : x = 3n, n ϵ N, and x < 4} = {3, 6, 9} Are not pairs of disjoint sets. 

(iv) G = {x : x ϵ N, x is even} and H {x : x ϵ N, x is prime} 

∵ 2 is an even prime number; their intersection is not Φ 

Are not pairs of disjoint sets. 

(v) J = {x : x ϵ N, x is even} and K = {x : x ϵ N, x is odd} 

∵ there is no number which is both odd and even. 

∴ J and K are pairs of disjoint sets.