Puzzle 32

The definition of a partition in Seven Sketches says:

> If \\(A\\) is a set, a partition of \\(A\\) consists of a set \\(P\\) and, for each \\(p \in A\\), a nonempty subset \\(A_p \subseteq A\\),

Maybe this wording is a bit off? This definition is saying a partition is the labeling set P with the subset of A. But this is just a subset of A and not a partition of A. If they are going to use labeling as the means, then the partition should just be the \\(\bigcup A_p\\)?