Which of the following sets are pairs of disjoint sets? Justify your a

1.	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» 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.

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»

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.