Question

Which of the following pairs of sets are disjoint?
$\left(i\right)\{1,2,3,4\}\text{and}\{x:x\text{is a natural number and}4\le x\le 6\}$
$\left(ii\right)\{a,e,i,o,u\}\text{and}\{c,d,e,f\}$
$\left(iii\right)\{x:x\text{is an even integer}\}\text{and}\{x:x\text{is an odd integer}\}$

Answer 1

$\left(i\right)\{1,2,3,4\}\text{and}\{x:x\text{is a natural number and}4\le x\le 6\}=\{4,5,6\}\because \{1,2,3,4\}\cap \{4,5,6\}=\left\{4\right\}$
Hence, pair of sets is not disjoint.

$\left(ii\right)\{a,e,i,o,u\}and\{c,d,e,f\}$
$\because \{a,e,i,o,u\}\cap \{c,d,e,f\}=\left\{e\right\}$
Hence, pair of sets is not disjoint

$\left(iii\right)\{x:x\text{is an even integer}\}=\{2,4,6,8,\dots \}\{x:x\text{is an odd integer}=\{1,3,5,7,\dots \}$
$\because \{2,4,6,8,...\}\cap \{1,3,5,7,...\}=\varphi$
Hence, pair of sets is disjoint.