Velleman writes Chapters 1 and 2 with logic and set theory braided together, on purpose. Chapter 1 is called “Sentential Logic,” but §1.3 and §1.4 are about sets; Chapter 2 is called “Quantificational Logic,” but §2.3 is about sets again. Sets are his worked example of the connectives: “x ∈ A or x ∈ B” is a disjunction, and A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) is the distributive law for ∧ and ∨ with “x ∈ —” wrapped around every letter.
In class I separate them: all of the propositional logic, then all of the predicate logic, then all of the set theory. Both orders cover exactly the same material, so read the book whichever way suits you — every problem is labelled with its section number.
| Velleman's order | Our order |
|---|---|
|
§1.1 connectives §1.2 truth tables §1.3 variables and sets §1.4 operations on sets §1.5 conditional, biconditional §2.1 quantifiers §2.2 quantifier equivalences §2.3 more operations on sets |
Unit I — Propositional Logic §1.1, §1.2, §1.5 Unit II — Predicate Logic §1.3 (first part only), §2.1, §2.2 (logic half) Unit III — Sets §1.3 (rest), §1.4, §2.2 (set half), §2.3 |
The tradeoff: you meet the ten equivalence laws in §1.2 and then wait two or three weeks before using them for anything. What you get back is that when the set operations do arrive you already have the whole logical toolkit, and §1.4 falls out of laws you know cold.
One thing we borrow early. Section 2.1 uses ∀x ∈ A and ∃x ∈ A, so we need the symbol ∈ before we build any set theory: A is a collection of things and x ∈ A means x is one of them. That is all we borrow.
Free and bound variables are introduced through quantifiers (§2.1) rather than through set-builder notation, which arrives in Unit III. If you are reading §1.3 straight through and hit set-builder notation before we have covered it, that is why.
§4.4 (ordering relations), §5.4 (closures), §6.2, §6.5, and Chapter 7 (number theory). Chapter 4 is taught only as far as equivalence relations require, and congruence modulo m is done inside §4.5, so you get modular arithmetic without Chapter 7.
§5.5 (images and inverse images) and Chapter 8 (infinite sets) are covered.
A handful of exercises inside sections we do cover depend on §4.4 or §5.4. They are not harder; they use vocabulary you will not have. Everything else in every section we cover is fair game.
Nothing in §6.1 is skipped. Several §6.4 exercises talk about the smallest element of a set; that is the well-ordering principle, which we cover in §6.4 itself, not the order theory of §4.4. Do those.
The problem list is on the course page, and the PDF carries the same list with commentary.