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 $B = C$
Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
$10 \, .........\, A $
Write the following as intervals :
$\{ x:x \in R,0\, \le \,x\, < \,7\} $
State which of the following sets are finite or infinite :
$\{ x:x \in N$ and ${x^2} = 4\} $