My doubt is relative to the power set and the notation.

If we have a set $A = \{a,b,c\}$, its power set is $$\mathcal{P}(A) = \{\emptyset,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},A\}$$

So we get rightly these notations

$a \in A$, $\{a\} \subset \mathcal{P}(A)$, $\{a\} \in \mathcal{P}(A)$?

Thanks in advance!