Question

Find the union of each of the following pairs of sets:
(i) $X=\{1,3,5\}Y=\{1,2,3\}$
(ii) $A=\{a,e,i,o,u\},B=\{a,b,c\}$
(iii) $A=\{x:x\text{is a natural number and multiple of}3\}$.
$B=\{x:x\text{is a natural number less than}6\}$.
(iv) $A=\{x:x\text{is a natural number and}1<x\le 6\}$

$B=\{x:x\text{is a natural number and}6<x<10\}$.
(v) $A=\{1,2,3\}$, $B=\varphi$

Answer 1

(i) $X=\{1,3,5\}Y=\{1,2,3\}$
$X\cup Y=\{1,2,3,5\}$
(ii) $A=\{a,e,i,o,u\}B=\{a,b,c\}$
$A\cup B=\{a,b,c,e,i,o,u\}$
(iii) $A=\{x:x\text{is a natural number and multiple of 3}\}$
$\Rightarrow A=\{3,6,9,12,15.....\}$
$B=\{x:x\text{is a natural number less than 6}\}$
$\Rightarrow B=\{1,2,3,4,5,6\}$
$\therefore A\cup B=\{x:x=1,2,4,5\text{or a multiple of 3}\}$
(iv) $A=\{x:x\text{is a natural number and}1<x\le 6\}$
$A=\{2,3,4,5,6\}$
$B=\{x:x\text{is a natural number and}6<x<10\}$
$B=\{7,8,9\}$
$A\cup B=\{x:xϵN$ and $1<x<10\}$
(v) $A=\{1,2,3\},B=\varphi$
$A\cup B=\{1,2,3\}$