If A and B are two sets such that $A\subset B$, then what is $A\cup B$?

Let $x\in A\cup B$ 
$\Rightarrow x\in Aorx\in B$
Since, $A\subset B$ 
$\Rightarrow x\in B$
But $x$ is an arbitrary element of set $A\cup B$.
$A\cup B\subset B$      ....(1)

Let $y\in B$
$\Rightarrow y\in A\cup B$   
But y is an arbitrary element of set B
$B\subset A\cup B$       ....(2)

From (1) and (2), we get
 $A\cup B=B$