Review for Final Exam

Math 8

Summer 2009           

Sections that will be covered: 2.9, 3.1-3, 4.1-3, 5.2, 5.3, 5.8, 6.3, 6.4

Go over all your old homework, quizzes and notes.

From each section:

2.9:

· Definitions: relation, reflexive, symmetric, transitive, inverse relation, equivalence relation, equivalence class, partition

· Show a given R is an (not) equivalence relation

· Understand link between partitions and equivalence classes

· Given the definition of some property for relations, be able to show that the relation has that property

3.1-3:

· Definitions: function, domain, image, range, codomain, map, inclusion map, identity map, constant map, equality of functions, restriction, extension, one-to-one, injective, onto, surjective, bijective, composition, commutative

· Given a function be able to show it has a given property (from the list above, or defined in the problem; eg. Injective or onto)

· Understand how to represent a function in set notation

· Know when a function has an inverse, and how to calculate it when possible

· Understand how composition works, when it is possible

· Be able to prove things like f and g onto, then f of g is onto. (There are lots of statements like this in 3.3)

4.1-3:

· Definitions: cardinality, finite, infinite, countable, uncountable

· Know how to show two sets have the same cardinality

· Know how to show #A <= #B

· Know how to show the reals, irrationals are uncountable

· Understand how you can combine countable sets and still be countable

· Be able to take a cardinality inequality and use the underlying injection to prove other inequalities (eg. #A < #B < #C => #A < #C)

5.2,3,8:

· Definitions: Sum rule, Product rule, permutation, n-set, k-subset, binomial coefficient, n choose k

· Be able to count sets that are counted using simple permutations or chooses

· Use the definition of n choose k to prove properties of it (nothing more than being able to write down the formulas and perform some basic algebra)

6.3-4:

· Definitions: k divides m ( k|m ), congruent mod m

· Use definitions to prove simple problems (things like 6.4 #3)

· Be able to calculate things like 1230 mod 7