equal sets

A set is decided by the own elements or members. Therefore, if every elements of two sets is according, two sets is equivalent. We shall some examples. The sets are as follows.

$A=\left\{ 1,2,3 \right\}$
$B=\left\{ 4,5,6 \right\}$
$C=\left\{ 1,2,3,4,5,6 \right\}$
$D=\left\{ 1,3,5 \right\}$
$E=\left\{ 2,4,6 \right\}$
$F=\left\{ 1,3 \right\}$
$G=\left\{ 2,4 \right\}$
$H=\left\{ 3,5 \right\}$
$I=\left\{ 6 \right\}$

Then, all below is true.

$A\cup B=C$ , $D\cup E=C$ , $F\cup G\cup H\cup I=C$ , 

$A\cup C=C$ , $B\cup C=C$ , $D\cup C=C$ , $E\cup C=C$ ,
$F\cup C=C$ , $G\cup C=C$ , $H\cup C=C$ , $I\cup C=C$ ,

$A\cap D=F$ , $B\cap E=G$ , $A\cap E=A\cap G$ , $B\cap D=B\cap H$ ,
$A\cup G=F\cup G$ , $E\cap H=G\cup H\cup I$ ,

Please note that, in elementary, overlapped elements should be deleted. i.e,
$A\cup F=\left\{ 1,1,2,3,3 \right\}=\left\{ 1,2,3 \right\}$