State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $(x - 1)(x - 2) = 0\} $

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and ${x^2} = 4\} $

If a set $A$ has $n$ elements, then the total number of subsets of $A$ is

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 $A \in C$

Assume that $P(A)=P(B) .$ Show that $A=B$.

Write the following sets in the set-builder form :

$\{ 1,4,9 \ldots 100\} $