Set theory pertaining to category theory and functional programming I'm reading an unfinished Introduction to Category Theory/Products and Coproducts of Sets and have come across the following:

A power set of a set is the set of all its subsets. A script 'P' is used for the power set. Note that the empty set and the set itself are members of the power set.
\begin{equation}\mathcal{P}\{1,2,3\} = \{\varnothing,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}\end{equation}
Set operations are functions from the product of a power set to a power set.
\begin{equation}\text{Union}:\mathcal{P}(X) \times \mathcal{P} \to \mathcal{P}(X), 
\text{Union}(A,B) = A \cup B\end{equation}

I don't understand the last part.
To me a product of a power set should equate to a set of tuples where the first of the ordered pair is a subset from first power set and the  second is a subset from the second power set. Whereas a power set is just a set of subsets.
How can this mismatch be explained or is it a mistake?

Taking on board the advice below:
If the set $X$ is a singleton value $1$, then:
\begin{equation}X = \{1\}\end{equation}
The power set of $X$ is then:
\begin{equation}\mathcal{P}(X) = \{\varnothing,\{1\}\}\end{equation}
The product of $\mathcal{P}(X)$ is then:
\begin{equation}\mathcal{P}(X)\times\mathcal{P}(X) = \{(\varnothing,\varnothing),(\varnothing,\{1\}),(\{1\},\varnothing),(\{1\},\{1\})\}\end{equation}
Applying $\text{Union}$ to the $\mathcal{P}(X)\times\mathcal{P}(X)$ is:
\begin{equation}\mathcal{P}(X)\times\mathcal{P}(X) = \{(\varnothing,\varnothing)\mapsto\varnothing,(\varnothing,\{1\})\mapsto\{1\},(\{1\},\varnothing)\mapsto\{1\},(\{1\},\{1\})\mapsto\{1\}\}\end{equation}
As the result is a set, duplicates can be removed:
\begin{equation}\{\varnothing,\{1\},\{1\},\{1\}\} = \{\varnothing,\{1\}\}\end{equation}
Thus:
\begin{equation}\mathcal{P}(X)\times\mathcal{P}(X) \to\mathcal{P}(X)\end{equation}
And so the set operation of $\text{Union}$, which is one of a family of set operations (a set of functions) is a function from the product of a power set to a power set
The notation $f:E\times F \to G$ means that $f$ is a function that needs two arguments, one from $E$, one from $F$, and the image is in $G$.
This is how the function $\text{Union}$ is defined: the two arguments $A$, $B$ are in $\mathcal{P}(X)$ and the image $\text{Union}(A, B) = A\cup B$ is in $\mathcal{P}(X)$.