State which of the following sets are finite or infinite :

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

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 $B = C$

Write the following as intervals :

$\{ x:x \in R,3\, \le \,x\, \le \,4\} $

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{ 3,4\}  \in A$

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 $x \in A$ and $A \not\subset B$, then $x \in B$

Write the following sets in roster form :

$A = \{ x:x$ is an integer and $ - 3 < x < 7\} $