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

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) $E=\{x: x \in N, x$ is even and $x<8\}$

$F=\{x: x=3 n, n \in N$, and $x<4\}$

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

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

Solution:

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) $E=\{x: x \in N, x$ 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) $G=\{x: x \in N, x$ is even $\}$ and $H\{x: x \in N, x$ is prime $\}$

$\because 2$ is an even prime number; their intersection is not $\Phi$

Are not pairs of disjoint sets.

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

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

∴ J and K are pairs of disjoint sets.