
What are the two types of reasoning we use in everyday life?
 1. Inductive reasoning
 2. Deductive reasoning

inductive reasoning
Inductive reasoning is the process of reasoning that arrives at a general conclusion or conjecture based on the observation of specific examples.
**Using specific examples to  arrive  at a general conclusion

deductive reasoning
Deductive reasoning is the process of reasoning that arrives at a specific conclusion based on previously accepted general statements.
** Arrive at a specific conclusion  via  previously accepted statements.

George Polya
FOUR major steps of problem solving
 1. Understand the problem
 2. Devise a plan
 3. Carry out the plan
 4. Look back, check the work

estimation
Estimation is the process of finding an approximate answer to a mathematical problem.
In many cases, it is not necessary to find the exact answer to a problem. When only an approximate answer is needed, you can use estimation. This is accopmplished by rounding the numbers used in the problem, then performing the necessary operatioin or operations.

define a set
A set is a welldefined collection of objects/elements.

What is meant when a set is well defined?
A set is said to be well defined when there is no misunderstanding as to whether or not an element belongs to a set.
Ex:the set of "letters of the English alphabet" is a welldefined set since it consists of the 26 symbols.
 The set of Great Lakes is {Ontario, Erie, Huron, Michigan, Superior}
 The days of the week are {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
 Write the set of natural numbers less than 6 {1, 2, 3, 4, 5}

Name the 3 ways to designate sets
 1. list or roster method
 2. descriptive method
 3. setbuilder method

Each object of a set is called...
an element or member of the set.

Write the set of natural numbers less than 8.
{1, 2, 3, 4, 5, 6, 7}

Write the descriptive of the set containing 2, 4, 6, 8, ...
Since the elements in the set are called the even natural numbers, the anser is:
E = even natural numbers

Use setbuilder notation to designate the set {2, 4, 6}
{ x  x ∈ E and x < 7 }
Reads: "The set of all x such that x is an even natural number and x is less than seven."

Use setbuilder notation to designate the set {red, yellow, blue}
{x  x is a primary color}
Reads: "The set of all x such that x is a primary color."

Designate the set 32, 33, 34, 35, ... using the roster method.
{32, 33, 34, 35, ...}

Designate the set 32, 33, 34, 35, ... using the descriptive method.
Natural numbers greater than 31.

Designate the set 32, 33, 34, 35, ... using the setbuilder notation.
{ x  x ∈ N and x > 31 }

finite set
A set is said to be a finite set if the number of elements contained in the set is either 0 or a natural number.

infinite set
A set is said to be an infinite set if it has an unlimited number of elements.

finite? or infinte?
{the natural numbers that are multiples of 6}
infinite

finite? or infinte?
{ x  x is a member of the U.S. Senate}
finite

finite? or infinte?
{3, 6, 9, ..., 24}
finite

null set
A set with no elements is called an empty set or null set. The symbols used to represent the null set are { } or circle w/line

Two sets are equal if...
they have exactly the same members or elements.

Two sets have a onetoone correspondence if and only if...
it is possible to pair the elements of one set with the elements of the other set in such a way that for each element in the first set there exists one and only one element in the second set.

What is a subset?
When all, some, or none of the elements of one set are used in another set, the second set is called a subset of the original set. Formally defined.
Ex: Subsets of {bacon, egg}
 {bacon, egg}
 {bacon}
 {egg}
 { }

What is a proper subset?
If a subset of a given set is NOT equal to the original set, then the subset is called a proper subset of the original set.
Original set: {bacon, egg}
{bacon, egg} ⊄ {bacon, egg} **Because it is equal to the original
{bacon}⊂ {bacon, egg}

What is the union of two sets?
All the elements of each set. Duplicates are not written twice.
Ex: A={10, 12, 14, 15} and B={13, 14, 15, 16, 17}
A ∪ B={10, 12, 13, 14, 15, 16, 17}

What is the intersection of two sets?
The set of elements that are common to both sets.
Ex: A={10, 12, 14, 15} and B={13, 14, 15, 16, 17}
A∩ B = {14, 15}

What is the complement of a set?
 It is the set of elements contained in the universal set that are NOT contained in the set noted.
 _
 A (the line over the set name denotes the compliment of that set)
 Basically everything outside of the mentioned set.

What is a Venn Diagram?
When a set or sets are represented pictorially using Venn Diagrams.

