|245||Chapter 1 Outline|
Sections, concepts, and problems
Section 1. Sets. The basics of sets, including subsets,
cardinatilty of finite sets, the standard number sets (natural numbers,
integers, rationals, reals), power sets, and collections of sets indexed
by another set.
Section 2. Set Operations. Intersections, unions, complements,
Cartesian products, DeMorgan's Laws for intersections and unions.
Section 3. Partitions. Partitions of nonempty sets into blocks.
Section 4. Logic and Truth Tables. Statemtents/propositions, truth
values of these, negations, conjunctions, disjunctions, DeMorgan's Laws
for sets and statements (and how they are related), the distributive laws
of "and" over "or" and vice-versa, truth tables, logical equivalence.
Section 5. Quantifiers.
The universal and existential quantifiers, their negations, how to
prove/disprove such statements, counterexamples, and more DeMorgan's Laws.
Section 6. Implications.
Implications and their: antecedents (hypotheses), consequences
(conclusions), converses, inverses, contrapositives, and negations. Also,
necessary and sufficient conditions.