Question

(i) If $A=\varphi$, find $n\left[P\right(A\left)\right]$
(ii) If $n\left(A\right)=3$, find $n\left[P\right(A\left)\right]$
(iii) If $n\left[P\right(A\left)\right]=512$ find $n\left(A\right)$

Answer 1

$\left(1\right)A=\varphi$

$m=0$ (number of elements)

$n\left[P\right(A\left)\right]=2^m$

$n\left[P\right(A\left)\right]=2^0$

$n\left[P\right(A\left)\right]=1$

$\left(2\right)n\left(A\right)=3$

$n\left[P\right(A\left)\right]=2^3$

$n\left[P\right(A\left)\right]=8$

$\left(3\right)n\left[P\right(A\left)\right]=512$

$n\left[P\right(A\left)\right]=2^m$

$512=2^m$

$m=9$

So, $n\left(A\right)=9$