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.
Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$
Write down all the subsets of the following sets
$\{ a\} $
Examine whether the following statements are true or false :
$\{ a\} \in \{ a,b,c\} $
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$