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

If $A = \{a, b, c, d, e, f\}$, then the number of subsets of $A$ which contains at least $2$ elements is

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

Write down all the subsets of the following set: $\{a\}$

Prove that for any sets $A$ and $B$,$A \cap (A \cup B) = A$.

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