Paulius: the problem says

> Let \$$P\$$ be the set of \$$(\sim)\$$-closed and \$$(\sim)\$$-connected subsets \$$(A_p)_{p \in P}\$$.

That's a bit of a mouthful, but the idea is this. If we start with an equivalence relation \$$\sim\$$ on a set \$$X\$$, we can use it to chop \$$X\$$ into a bunch of parts called 'equivalence' classes:

\$$P\$$ is the set of these parts. It's a bit ridiculous to say "the set of subsets \$$(A_p)_{p \in P}\$$". One can equivalently just say \$$P\$$, since this is the same thing!

If you're wondering what a " \$$(\sim)\$$-closed and \$$(\sim)\$$-connected subset" is, you can ask me or look it up in the book - it's in the proof of Proposition 1.11, right before this exercise.

The point of the exercise is to show that these "\$$(\sim)\$$-closed and \$$(\sim)\$$-connected subsets" really do form a partition of \$$X\$$.