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(i) $X = \{ 1,3,5\} Y = \{ 1,2,3\} $

(ii)$A = \{ a,e,i,o,u\} ,B = \{ a,b,c\} $

(iii)$A = \{ x:x$ is a natural number and multiple of $3\} $

$B = \{ x:x$is a natural number less than $6\} $

(iv)$A = \{ x:x$ is a natural number and $1 < x \leqslant 6\} $

$B = \{ x:x$is a natural number and $6 < x < 10\} $

(v) $A = \{ 1,2,3\} ,B = \phi $

Answer
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(i) the given sets are:

$

X = \{ 1,3,5\} \\

Y = \{ 1,2,3\} \\

$

Now, we will find union of $X,Y$, we have

$X \cup Y = \{ 1,2,3,5\} $

(ii) Sets are:

$A = \{ a,e,i,o,u\} $

$B = \{ a,b,c\} $

Now, we will find the value of union $A,B$ we have

$A \cup B = \{ a,b,c,e,i,o,u\} $

(iii) sets are: $A = \{ x:x$is a natural number and multiple of $3\} $

$B = \{ x:x$ is a natural number less than $6\} $

Now, Natural numbers $ = 1,2,3,4,5,6,7,8,9,10$…..

And multiple of $3 = 3,6,9,12,15,....$

So, $A = \{ 3,6,9\} $and $B = \{ 1,2,3,4,5\} $

Now, we will find the union of $A\,and\,B$ set, so

$A \cup B = \{ 1,2,3,4,5,6,9\} $

$A \cup B = \{ x:x$ is a natural number, $x = 1,2,3,4,5$ or a multiple of $3\} $

(iv) $A = \{ x:x$ is a natural number and $1 < x \leqslant 6\} $

$B = \{ x:x$ is a natural number and $6 < x < 10\} $

So, $A = \{ 2,3,4,5,6\} $

$B = \{ 7,8,9\} $

Now, $A \cup B = \{ 2,3,4,5,6,7,8,9\} $

$\therefore A \cup B = \{ x:x \in N$ and $1 < x < 10\} $

(v) $A = \{ 1,2,3\} $

$B = \phi \,or\,\{ \,\} \,$

So, $A \cup B = \{ 1,2,3\} $

Natural numbers$ = \{ 1,2,3,4,5,......\} $

Whole numbers $ = \{ 0,1,2,3,4,....\} $

Integers numbers $ = \{ - 4, - 3, - 2, - 1,0,1,2,3,.....\} $

Find the union of sets in accordance to the type of number which the set contains(ie whether natural,real or whole numbers)