"You uttered your words as if you do not recognize shadows, or evil either. But would you be so good as to reflect on the question: what would your good do if evil did not exist, and what would the earth look like if shadows disappeared from it?" M. Bulgakov, "The Master and Margarita"
If the world couldn't be divided into classes, we couldn't tell objects, events or relations apart at all — the universe would collapse into a single point. Level A2 builds the machinery for that division: what a mathematical concept actually is, how logic and naive set theory turn out to be two sides of one coin, and how relations sharpen into orders, equivalences and functions.
The chapter opens with Woland's rebuke to a character in Bulgakov who wants good without evil, light without shadow — and uses it to make a formal point: if everything we could possibly describe couldn't be split into at least two classes, we could never tell objects, events, or relations apart. Logic, in the broadest sense used here, is exactly the complex of rules that lets us draw those distinctions — separate the essential from the accidental, and find structure in a body of knowledge.
But a naive "correct lexemes are true, everything else is false" logic of syntax alone isn't enough: it can recognize well-formed expressions but says nothing about the world they describe. What's needed is a four-stage recipe — build a language fragment, define its terms and formulas, fix rules of inference, and declare a starting set of axioms — the same scheme the rest of the book keeps re-applying to new subject domains.
Once truth and falsity are pinned to the satisfaction of a predicate, a striking pattern falls out: every logical connective used to define a new concept corresponds exactly to a set-theoretic operation on its extension.
The first three are immediate: define a concept as "$a$ satisfies $\mathcal D_1$ and $\mathcal D_2$" and its extension is exactly $V_1\cap V_2$; swap and for or and intersection becomes union. Implication is the interesting case, precisely because mathematics defines it so differently from everyday speech: the formula $\mathcal D_1(a)\to\mathcal D_2(a)$ is true not only when both properties hold, but also for every $a$ that simply fails $\mathcal D_1$ — vacuously true, the way "if it rains, the ground is wet" is trivially true on a sunny day. Work out the extension carefully and implication corresponds to $(\mathcal U\setminus V_1)\cup V_2$; only in the special case where the implication is a tautology does it collapse to plain inclusion, $V_1\subseteq V_2$.
That correspondence is why the chapter can introduce a full toolkit of relations almost for free. A relation is just a set of tuples $\langle x,y\rangle$ satisfying some property, and depending on which of reflexivity, symmetry, transitivity and antisymmetry it has, it earns a name: an equivalence relation (all three of the first) partitions a universe into classes — "having the same father" splits people into sibling groups; a reflexive, antisymmetric, transitive relation is a partial order; add connexity and it's a linear order. A relation that is total and single-valued is simply a function — the familiar $f:A\to B$ is just a very disciplined kind of set.
The first five exercises from the chapter's problem set, from the English edition.
Level A2 has 22 exercises in total, each with a full worked solution in the book's appendix.