Question

Find the union of each of the following pair of sets:
$\left(i\right)x=\{1,3,5\},y=\{1,2,3\}$
$\left(ii\right)A=\{a,e,i,o,u\},B=\{a,b,c\}$
$\left(iii\right)A=\{x:x\text{is a natural number and multiple of}3\}B=\{x:x\text{is a natural number less than}6\}$
$\left(iv\right)A=\{x:x\text{is a natural number and}1<x\le 6\}B=\{x:x\text{is a natural number and}6<x<10\}$
$\left(v\right)A=\{1,2,3\},B=\varphi$

Answer 1

Given: $x=\{1,3,5\},y=\{1,2,3\}$
The union of $x$ and $y$ is the set which consists of all the elements of $x$ as well as $y$, the common elements being taken only once.
$\therefore x\cup y=\{1,2,3,5\}$

Given: $A=\{a,e,i,o,u\},B=\{a,b,c\}$
The union of $A$ and $B$ is the set which consists of all the elements of $A$ as well as $B$, the common elements being taken only once.
$\therefore A\cup B=\{a,b,c,e,i,o,u\}$

Given: $A=\{x:x\text{is a natural number and multiple of}3\}$
$\therefore A=\{3,6,9,12,\dots \}$
$B=\{x:x\text{is a natural number less than}6\}$
$\therefore B=\{1,2,3,4,5\}$
Hence, $A\cup B=\{1,2,3,4,5,6,9,12,...\}$
or $A\cup B=\{x:x=1,2,3,4,5\text{or a multiple of}3\}$

Given: $A=\{x:x\text{is a natural number and}1<x\le 6\}$
$\therefore A=\{2,3,4,5,6\}$
$B=\{x:x\text{is a natural number and}6<x<10\}$
$\therefore B=\{7,8,9\}$
Hence, $A\cup B=\{2,3,4,5,6,7,8,9\}$
or $A\cup B=\{x:x\in N\text{and}1<x<10\}$

Given: $A=\{1,2,3\},B=\varphi$
The union of $A$ and $B$ is the set which consists of all the elements of $A$ as well as $B$, the common elements being taken only once.
$\therefore A\cup B=\{1,2,3\}$