# How do I take the power set of a set of ordered pairs?

I have $P(\left\{ 4,5 \right\}\times\left\{ 1 \right\} )$

I found the cartesian product within the parameter of the power set, but now I don't know how to take the power set of the ordered pairs.

$$P(\left\{ (4,1),(5,1) \right\} )$$

I did some searching, and I found this: Ordered pairs in a power set.

However, it does not help me with what I'm wondering about. Or, I just don't understand the terminology used there by the OP and answerers.

First write down $\{4,5\}\times\{1\}$ correctly: It is the set containing the two pairs $(4,1)$ and $(5,1)$, so it is $\{(4,1),(5,1)\}$. Then the power set is the set of all subsets. The subsets are the empty set, the two one-element sets, and the full set, so $$\mathcal P(\{4,5\}\times\{1\}) =\bigl\{\emptyset,\{(4,1)\},\{(5,1)\},\{(4,1),(5,1)\}\bigr\}.$$
Hint: If $x=(4,1)$ and $y=(5,1)$, then you have $X=\{x,y\}$. Can you determine $P(X)$ from here?