Let A, B and C be three sets. If $A\in B$and $B\subset C$. is it true that $A\subset C$? If not give an example.

Solution: Let there is an element $a$ in set A.Then,
$a\in A$.
Now, as $A$ is a subset of $B$ as we are given, $A\subset B$. It means element $a$ should also be in $B$.
$a\in B$
Now, as $B$ is a subset of $C$ as we are given, $B\subset C$. It means element $a$ should also be in $C$.
$a\in C$
Thus, we can say that, $A\subset C$We have assumed it for a single element $a$. But, there can be many elements in Set $A$ that will satisfy the given condition.