Odisha Board Solutions for Chapter: Sets, Exercise 1: Exercises- 2(a)

For any object $x$, there is a set $A$ such that $x\in A$.

For every object $x$, there is a set $A$ such that, $x\notin A$.

$a\in \left\{\right\{a,b\},b\},a\ne b$

If $A$ is a proper subset of $B$ and $B$ is a subset of $C$, then $A$ is a proper subset of $C$.

$A\subset \varphi$ if and only if $A=\varphi$.

Find the number of elements of:

$\mathrm{P}\left(\mathrm{P}\right(\varphi \left)\right)$

Find the number of elements of:

$P\left(P\right(P\left(\varphi \right)\left)\right)$

Find the number of elements of:

$P\left(P\right(P\left(P\right(\varphi \left)\right)\left)\right)$