The number of proper subsets of the set $\{1, 2, 3\}$ is

Write the following intervals in set-builder form :

$\left( { - 3,0} \right)$

State which of the following sets are finite or infinite :

$\{ x:x \in N$ and $x$ is prime $\} $

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 $A \not\subset B$ and $B \not\subset C,$ then $A \not\subset C$

State which of the following sets are finite or infinite :

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

Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$