Question

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

Answer 1

(i) $A=\{1,2,3,4\}$
$B=\{x:x\text{is a natural number and}4\le x\le 6\}=\{4,5,6\}$
Now, $A\cap B=\{1,2,3,4\}\cap \{4,5,6\}=\left\{4\right\}$
Therefore, this pair of sets are not disjoint.
(ii) $A=\{a,e,i,o,u\}$
$B=\{c,d,e,f\}$
$A\cap B=\left\{e\right\}$
Therefore, this pair of sets are not disjoint.
(iii) $A=\{x:x\text{is an even integer}\}$
$B=\{x:x\text{is an odd integer}\}$
$A\cap B=\varphi$
Therefore, this pair of sets is disjoint.