1. Propositional logic:

(a) Know truth tables for ¬,∧,∨,→,↔, and be able to build truth tables for compound propositions.

(b) Negations (2.1.3).

(c) Conditional rules (2.1.3).

2. Quantifiers (2.2.2):

(a) Limiting: ∀x(W(x) → C(x)) and ∃y(W(x) ∧ C(x)).

(b) Proposition 4,5: Difference between ∀x∃yK(x, y) and ∃y∀xK(x, y).

(c) HW 3.

(d) Negation: Proposition 2,3.

(e) Express at least, at most, and exactly.

3. Proofs:

(a) Direct proofs: Propositions 8, 23∗, HW 4, 5.

(b) Contraposition: Proposition 10∗, HW 6. √

(c) Proof by contradiction: Proposition 13∗, 3 2 is irrational, Proposition 36∗, use with LEA.

(d) Proof by cases Proposition 15.

(e) Proofs of equivalence: Proposition 16.

(f) Existence proofs: Propositions 17, 18, 20, Theorem 28∗.

(g) LEA: Proposition 21, HW 7, 8; Theorem 24∗ for a ≥ 0; Lemma 27∗.

(h) Induction: Theorem 36∗; Proposition 37, HW 7, 8; Lemma 38∗; Theorem 39, 40, HW 11.