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 $x \notin B,$ then $x \notin A$
Which of the following sets are finite or infinite.
$\{1,2,3, \ldots 99,100\}$
Write the set $\{ x:x$ is a positive integer and ${x^2} < 40\} $ in the roster form.
Write down all the subsets of the following sets
$\{ 1,2,3\} $
Write the set $A = \{ 1,4,9,16,25, \ldots .\} $ in set-builder form.