SECTION

4.1: Defining Sets and Tuples

Subsets, proper subsets, the empty set

Cardinality

Sequences

By listing the elements 

By giving a property which describes the elements  

pg.81-83:
#1, 2, 3, 4, 5, 6, 7, 8, 9

pg.92-94: #1, 2, 4, 8, 9, 10, 12, 13, 15

Complement, union, intersection, difference

k-subsets

Cartesian product, ordered pairs

DeMorgan's Laws for sets 

Venn diagrams 

Inclusion-Exclusion 

Pigeonhole Principle

pg.95-97:
#1, 2, 3, 4, 5, 6, 7, 8, 9

pg.104-106:
#1, 2, 3, 4, 5, 6, 9, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28

Predicates

Existential: looping through a set to see if some element has a certain property 

Universal: looping through a set to see if all elements have a certain property  

Proving and disproving quantified statements

Venn diagrams of quantified statements

Negations of quantified statements

pg.107-110:
#1, 3, 4, 5, 6, 7, 8

pg.117-120:
#1, 3, 4, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19

5.2: Multiple Quantifiers

Proving and disproving statements with two quantifiers

Onto functions

One-to-one functions

Interpreting statements with two quantifiers

Negating these statements

pg.121-123:
#3, 4, 5, 6, 7

pg.133-136:
#1, 3, 5, 6, 9, 10, 11, 12, 14, 17, 18, 19

6: Mathematical Induction

Predicates as functions

Base Case

Recursive functions

Fibonacci numbers

Creating the implication

Coordinating an induction proof

pg. 137-139:
#1, 5, 6, 7, 8

pg. 147-149: #1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22