Obtain the order of each element of $\wp (S)$, where $S=\{1,2,3\}$

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I am unsure what $\wp (S)$ means in this question. But I assume this is power set of the set $S$.

We know that power set is a group under the operation $ \triangle$ which is symmetric difference of two sets.

Let $G=\wp (S)$

$\emptyset$ is the identity element in $G$. Now let $A \in G$ be any subset of $S$ then $A \triangle A=(A- A) \cup (A- A)=\emptyset \cup \emptyset=\emptyset $. So $\vert A \vert=2$.

And We can conclude that every member of $G$ has order $2$. Also this is true regardless of the cardinality of the set $S$.

Please let me know if $\wp (S)$ means powser set in this context and whether I have followed right approach.