How many elements has $P(A),$ if $A=\varnothing ?$

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

$\{ x:x$ is an even natural mumber $\} \ldots \{ x:x$ is an integer $\} $

State whether each of the following set is finite or infinite :

The set of circles passing through the origin $(0,0)$

For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?

- [KVPY 2013]

Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.