Math 1120B Winter 2014
Chapter 8
Sections 8.1 and 8.2. Relations and Properties of Relations
We are already familiar with several types of relations in mathematics: x = y,
x < y, x > y, x y mod n, A B
Math 1120B Winter 2014
Chapter 6
Sections 6.1 and 6.2. Mathematical Induction
Let A be a non-empty set of real numbers. An element m A is called a least
element or minimum if a A, a m.
Example: The su
Math 1120B Winter 2014
Chapter 5
Section 5.1. Existence and Proof by Contradiction
Some statements of the form x D, R(x) are false, which is equivalent to saying
that some statements of the form x D,
Math 1120B Winter 2014
Chapter 2
Section 2.1. Logic
A statement is a declarative sentence which is either true or false (but not both).
Every statement has a truth value, namely true or false. The let
Math 1120B Winter 2014
Chapter 3
Section 3.1. Trivial and Vacuous Proofs
A statement which is taken to be true without proof for the purposes of making
an argument is called an axiom. A statement whos
Practice Problems For Midterm I
Note: These problems are intended for practice for the exam. Do not assume
that items not covered in these problems will not be tested. The midterm
will cover Chapters
Review for Midterm II
Note: Warning, this is probably not exhaustive and probably does contain
typos (which Id like to hear about), but represents a review of most of the
material covered in Chapters
Math 1120B Winter 2014
Chapter 9
Sections 9.1 and 9.2. Functions
Suppose A and B are sets. A function f : A B from A to B is a relation
f A B such that every element a A is the rst coordinate of exact
Math 1120B Winter 2014
Chapter 4
Section 4.1. Proofs Involving Divisibility of Integers
Given two integers a and b with a = 0, we say that a | b or in words a divides b
whenever there is an integer c
Review for Final Exam
Note: Warning, this is probably not exhaustive and probably does contain
typos (which Id like to hear about), but represents a review of most of the
material covered in Chapters