Sections, concepts, and problems

1.1. Logic. Propositions, negations, conjunctions, disjunctions (and exclusive or's), implications (and their hypotheses and conclusions), biconditionals, Boolean variables.
1, 5, 7, 11, 15a-d, 19, 21a-d, 25a, 29, 34, 35, 37

1.2. Propositional equivalences. Logical equivalence, using truth tables to show whether two compound propositions are logically equivalent, various laws of logic ("famous" logical equivalences), some of which are particularly useful in proving things.
5, 7d, 15, 30-33

1.3. Predicates and quantifiers. Propositional functions, free and bound variables, the existential and universal quantifiers, how to negate propositions which contain quantifiers.
3, 5, 9, 21, 25, 31, 45

1.4. Sets. Sets and their elements, set-builder notation, subsets, set equality, proper subsets, cardinality of a set, power set of a set, the Cartesian product of sets.
1, 3c, 5cd, 7, 15, 17, 27

1.5. Set operations. Unions, intersections, differences, and complements of sets; disjoint sets.
3, 9, 13, 15c, 19, 21, 31, 35, 39 (see Example 17)

1.6. Functions. Functions, domains, codomains, image of an element or set, inverse image of an element or set (done in class, not in the section), injections, surjections, bijections, stictly increasing/decreasing functions from (some subset of) the reals to (some subset of) the reals, addition and multiplication of functions with codomain some subset of the reals, inverses of bijections, composite functions.
1c, 7 (see Def. 12), 8, 9, 13, 15abc, 19, 25, 28, 55, 57a

1.7. Sequences and summations. Sequences, strings, arithmetic and geometric progressions, summations, cardinality, countable and uncoutable sets.
3abc, 5adfg, 9ce, 13d (see 19), 15a, 19, 23, 29, 31

1.8. The growth of functions. Determining "eventual" upper and lower bounds for functions. Big-O, big-Omega, and big-Theta notations are introduced.
1, 3, 5, 7ab, 9, 15, 17, 19ab, 27

Other Chapters

Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 6