Reading Set Expression as it is Spoken

Question

I am reading a paper pertaining to TSP and came with the following paragraph:

I want to ask how to read the union expression in the above paragraph, why are there two $P_k$? So inorder to read it out does it say

All Union of $P_k$ element of $L$, we form the set of vertices?

If that is so how to intrepret the two $P_k$'s?

Answer 1

Each $P_k$ is a subset of nodes, and $V$ (not defined in the quoted paragraph) is presumably the full node set in the original graph. The equality says that the nodes in the paths $P_k$ together cover all nodes in $V$. The $P_k$ in the subscript is an index. It might have been less confusing to write the union as $\cup_{k=1}^{|\mathcal{L}|} P_k$.

Answer 2

I would read it as 'The union over all elements $P_{k}$ in $L$'.