If $A\cup B=B$, does it follows that $A \subseteq B$? We know that $A \subseteq B \Rightarrow A \cup B = B$. Is the theorem valid in the other direction $\Leftarrow$? 
I thought of it to be intuitive that the $\Leftarrow$ direction should be valid too. Is it?


Given : $A\cup B = B$
Since $A\cup B$ contains all elements of $A$, $B$ should also contain all elements of $A$. Hence $A\subseteq B$
