Write the following sets in roster form :

$C = \{ x:x{\rm{ }}$ is a two-digit natural number such that sum of its digits is $8\} $

Examine whether the following statements are true or false :

$\{a\} \subset\{a, b, c\}$

Which of the following are sets ? Justify your answer.

The collection of all even integers.

Write the following sets in the set-builder form :

${\rm{\{ 2,4,8,16,32\} }}$

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 $A \subset B$ and $B \in C,$ then $A \in C$

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