Question

In the following, state whether $A=B$ or not:
$\left(i\right)A=\{a,b,c,d\}B=\{d,c,b,a\}$
$\left(ii\right)A=\{4,8,12,16\}B=\{8,4,16,18\}$
$\left(iii\right)A=\{2,4,6,8,10\}B=\{x:x$ is positive even integer and $x\le 10\}$
$\left(iv\right)A=\{x:x$ is a multiple of $10\}B=\{10,15,20,25,30,...\}$

Answer 1

$\left(i\right)$ Every element present in $A$ is also in $B$ and every element present in $B$ is also in $A.$
Since order in which the elements of a set are listed, is not significant
$\therefore A=B$

$\left(ii\right)$ We observe that $12\in A$ but $12\notin B$
$\therefore A\ne B$

$\left(iii\right)$ Given $:A=\{2,4,6,8,10\}$ and $B=\{x:x$ is positive even integer and $x\le 10\}=\{2,4,6,8,10\}$
Every element present in $A$ is also in $B$ and every element present in $B$ is also in $A.$
$\therefore A=B$

$\left(iv\right)A=\{x:x$ is a multiple of $10\}$
So, $A=\{10,20,30,40,50,...\}$
and $B=\{10,15,20,25,30,...\}$
Here , $15\in B$ but $15\notin A$
$\therefore A\ne B$