State which of the following sets are finite or infinite :

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

The number of non-empty subsets of the set $\{1, 2, 3, 4\}$ is

Write the following as intervals :

$\{ x:x \in R,0\, \le \,x\, < \,7\} $

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 $B = C$

Which of the following are sets ? Justify your answer.

The collection of ten most talented writers of India.

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 $x \in B$