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 $\}$
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.
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