Let $S = \{ 0,\,1,\,5,\,4,\,7\} $. Then the total number of subsets of $S$ is

- A
$64$

- B
$32$

- C
$40$

- D
$20$

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\} \ldots \{ x:x$ student of your school $\} $

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 $B \subset C,$ then $A \subset C$

In rule method the null set is represented by

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a circlein the plane $\} \ldots \{ x:x$ is a circle in thesame plane with radius $1$ unit $\} $

State which of the following sets are finite or infinite :

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