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\$$?