Question

State whether each of the following statement is true or false. Justify your answer.
(i) {$2,3,4,5$} and {$3,6$} are disjoint sets.
(ii) {$a,e,i,o,u$} and {$a,b,c,d$} are disjoint sets
(iii) {$2,6,10,14$} and {$3,7,11,15$} are disjoint sets
(iv) {$2,6,10$} and {$3,7,11$} are disjoint sets

Answer 1

(i) False
$A=\{2,3,4,5\}$ $B=\{3,6\}$
$\Rightarrow A\cap B=\left\{3\right\}$
So, A and B are not disjoint sets.
(ii) False
$A=\{a,e,i,o,u\}$ , $B=\{a,b,c,d\}$
$A\cap B=\left\{a\right\}$
Hence, A and B are not disjoint sets.
(iii) True
$A=\{2,6,10,14\}$ ,$B=\{3,7,11,15\}$
$A\cap B=\varphi$
Hence, A and B are disjoint sets.
(iv) True
$A=\{2,6,10\}$ ,$B=\{3,7,11\}$
$A\cap B=\varphi$
Hence, A and B are disjoint sets.