Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:

$ 4\, ......... \, A $

Which of the following are sets ? Justify your answer.

A team of eleven best-cricket batsmen of the world.

Let $A=\{a, e, i, o, u\}$ and $B=\{a, i, u\} .$ Show that $A \cup B=A$

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.

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m \times n$ is

Examine whether the following statements are true or false :

$\{ a,e\}  \subset \{ x:x$ is a vowelin the English alphabet $\} $