1. Propositional Logic Defining Propositional Logic
Propositions
Connectives
Truth tables
Precedence of Logical Operators
Usefulness of Logic
Bitwise operations
Logic in Theoretical Computer Science (SAT)
Logic in Programming
Logical Equivalences
Terminology
Equivalence rules

2. Predicate Logic Introduction Terminology: Quantifiers
Propositional functions; arguments; arity; universe of discourse
Quantifiers
Definition; using, mixing, negating them
Logic Programming (Prolog)
Transcribing English to Logic

3. Proofs Terminology Rules of inference: Fallacies
Modus ponens, addition, simplification, conjunction, modus tollens, contrapositive, hypothetical syllogism, disjunctive syllogism, resolution,
Examples
Fallacies
Proofs with quantifiers
Types of proofs:
Trivial, vacuous, direct, by contrapositive (indirect), by contradiction (indirect), by cases, existence and uniqueness proofs; counter examples
Proof strategies:
Forward reasoning; Backward reasoning; Alerts

4. Sets Definitions: set, element Terminology and notation
Set equal, multi-set, bag, set builder, intension, extension, Venn Diagram (representation), empty set, singleton set, subset, proper subset, finite/infinite set, cardinality
Proving equivalences
Power set
Tuples (ordered pair)
Cartesian Product (a.k.a. Cross product), relation
Quantifiers
Set Operations (union, intersection, complement, difference), Disjoint sets
Set equivalences (cheat sheet or Table 1, page 124)
Inclusion in both directions
Using membership tables
Generalized Unions and Intersection
Computer Representation of Sets

5. Functions Definitions & terminology Properties
function, domain, co-domain, image, preimage (antecedent), range, image of a set, strictly increasing, strictly decreasing, monotonic
Properties
One-to-one (injective), onto (surjective), one-to-one correspondence (bijective)
Exercices (5)
Inverse functions (examples)
Operators
Composition, Equality
Important functions
identity, absolute value, floor, ceiling, factorial