math 210 finite mathematicsmath.niu.edu/~richard/math210/overview.s10.pdfmath 210 finite mathematics...

Math 210 Finite Mathematics• Section 1

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• Spring, 2010

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• Spring, 2010

• Mon, Wed, Fri

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• Spring, 2010

• Mon, Wed, Fri

• 10:00 - 10:50 p.m.

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• Spring, 2010

• Mon, Wed, Fri

• 10:00 - 10:50 p.m.

• Faraday Hall 143

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• Spring, 2010

• Mon, Wed, Fri

• 10:00 - 10:50 p.m.


• Professor Richard Blecksmith

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• Spring, 2010

• Mon, Wed, Fri

• 10:00 - 10:50 p.m.



• Dept. of Mathematical Sciences

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• Spring, 2010

• Mon, Wed, Fri

• 10:00 - 10:50 p.m.



• Dept. of Mathematical Sciences

• Northern Illinois University

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Instructor InfoProfessor Richard Blecksmith

• Office: 344 Watson Hall

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• email: [email protected]

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• phone: 815-753-1835

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• phone: 815-753-1835

• hours: Mon, Wed 11:00 - 11:50Wed 2:00 - 2:50

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• phone: 815-753-1835

• hours: Mon, Wed 11:00 - 11:50Wed 2:00 - 2:50

• or by appointment

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• phone: 815-753-1835

• hours: Mon, Wed 11:00 - 11:50Wed 2:00 - 2:50

• or by appointment

• webpage: http://math.niu.edu/courses/math210

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Important Dates

• Martin Luther King Holiday is Mon Jan 18

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Important Dates


• Spring Break: Sat Mar 6 – Sun Mar 14

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Important Dates



• Last Day to Withdraw Fri March 5

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Important Dates



• Last Day to Withdraw Fri March 5

• Final Exam Monday, May 3, 8 - 9:50 p.m.

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Recitation• Teaching Assistant: Chris Bailey

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Section Day Time Room

1 Tues 10-10:50 DU 348

3 Tues 11-11:50 DU 300

5 Thurs 10-10:50 DU 302

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1 Tues 10-10:50 DU 348

3 Tues 11-11:50 DU 300

5 Thurs 10-10:50 DU 302

• Teaching Assistant: Necole McGary

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1 Tues 10-10:50 DU 348

3 Tues 11-11:50 DU 300

5 Thurs 10-10:50 DU 302

• Teaching Assistant: Necole McGary

•


2 Tues 10-10:50 DU 328

4 Tues 11-11:50 DU 328

6 Thurs 11-11:50 DU 302

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Course Info• Text: Finite Mathematics

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• NIU edition or standard paperback edition

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• S. T. Tan

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• S. T. Tan

• Calculator Policy: Basic Scientific or GraphingCalculators will be allowed on the exams

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• S. T. Tan

• Calculator Policy: Basic Scientific or GraphingCalculators will be allowed on the exams

• You may use a calculator which cancommunicate with other calculators or hasinternet capabilities on the exams

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Tests• Three Tests

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• Test Dates:Test 1: Wed, Feb 10Test 2: Fri, Mar 5 (before spring break)Test 3: Mon, Apr 19

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• Test Dates:Test 1: Wed, Feb 10Test 2: Fri, Mar 5 (before spring break)Test 3: Mon, Apr 19

• Final Exam Monday May 3, 8 - 9:50 p.m.

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Point Distribution• Each Test is worth 90 points

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• Final Exam is worth 150 points

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• Recitation Quizzes are worth 100 points

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• Homework is worth 50 points

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• Attendance quizzes (during class) are worth 30points

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• Attendance quizzes (during class) are worth 30points

• Total: 600 points

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Grading Curve

• Your percentage in the class is

Total Points

6

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Grading Curve


Total Points

6

• The grading curve is based on your finalpercentage in the class

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Grading Curve


Total Points

6


• The grading curve is at least as generous as

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Grading Curve


Total Points

6



• A 85%

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Grading Curve


Total Points

6



• A 85%• B 75%

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Grading Curve


Total Points

6



• A 85%• B 75%• C 60%

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Grading Curve


Total Points

6



• A 85%• B 75%• C 60%• D 50%

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Some Advice• Especially if you are repeating the course

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The Pass—for—Flunkers Program

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How to Pass the CourseTo get a C in this course, turn in the all the homeworkand study for the quizzes and show up for theattendance quizzes

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• Homework: 48 pts / 50

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• Recitation Quizzes: 80 pts / 100

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• Attendance Points: 27 pts / 30

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• Attendance Points: 27 pts / 30


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How to Pass the Course IINow suppose you know how to solve 36% of the testquestions:

• 36% of 420 = 151.2 points

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• 36% of 420 = 151.2 points

• Guess on the remaining 268.8 points

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• 36% of 420 = 151.2 points


• The probability of guessing correctly is 1/5

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• 36% of 420 = 151.2 points



• 1/5 of 268.8 = 53.8 points

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• 36% of 420 = 151.2 points



• 1/5 of 268.8 = 53.8 points


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• 36% of 420 = 151.2 points



• 1/5 of 268.8 = 53.8 points


• 155 + 205 = 360, the guaranteed cutoff for a C.

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Observations• This strategy requires that you:

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• work very hard on the non test part of thecourse

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• know something (36% of the material)

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• know something (36% of the material)• are an average guesser

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• The secret is to

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• get as many easy points as you can

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• get as many easy points as you can• come to class and recitation regularly

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• get as many easy points as you can• come to class and recitation regularly• work consistently

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Syllabus

• Chapters 6 and 7 Sets, Counting, Probability

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Syllabus


• Chapters 1 and 2 Linear Systems and Matrices

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Syllabus



• Chapters 3 and 4 Linear Programming and theSimplex Method

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Syllabus



• Chapters 3 and 4 Linear Programming and theSimplex Method

• Chapter 5 Basic Finance

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Homework• The complete homework list may be found at the

website

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website

• http://math.niu.edu/math210

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website


• Go to the section titled Homework Problems

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website



• To get started today, the first assignment is

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website




• Section 6.1, page 320, Sets & Set Operations.

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website





• Exercises 6, 9–12, 28, 32, 38, 48, 62, 70

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website





• Exercises 6, 9–12, 28, 32, 38, 48, 62, 70

• Exercises from Chapter 6 are currently on line

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OverviewFour typical problems you will learn to solve thissemester:

• counting

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• counting

• probability

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• counting

• probability

• expectation

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• counting

• probability

• expectation

• linear programming

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Counting

A market survey of smoking habits of 100 personsshowed that

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Counting


• 18 smoked only a pipe

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Counting



• 23 smoked pipes, but not cigarettes

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Counting




• 8 smoked pipes and cigars

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Counting





• 26 smoked pipes

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Counting





• 26 smoked pipes

• 8 smoked both cigars and cigarettes

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Counting





• 26 smoked pipes


• and 24 deep-breathing souls smoked not at all.

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Counting





• 26 smoked pipes



• How many cigarette smokers were in thissample?

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Counting





• 26 smoked pipes



• How many cigarette smokers were in thissample? [Answer: 18]

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Counting





• 26 smoked pipes




• Is there a market for a combination pipe andcigarette holder in this sample?

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Counting





• 26 smoked pipes




• Is there a market for a combination pipe andcigarette holder in this sample? [Answer: no]

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Probability

A healthcare example:

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Probability


• A particular chest x-ray technique detects TB 90of the time

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Probability



• but 1% of the time incorrectly indicates theexaminee has TB

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Probability




• Assume the incidence of TB is 5 persons per10,000

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Probability





• A person selected randomly tests positive on thex-ray

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Probability






• What is the probability the person has TB?

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Probability






• What is the probability the person has TB?

• Answer 4.5%

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Linear Programming

A furniture refinishing plant finishes two type oftables: regular and deluxe. Each table must be sanded,stained, and varnished.

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Linear Programming


• A standard table requires 5 minutes of sanding,12 minutes of staining, and 9 minutes ofvarnishing.

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Linear Programming



• A deluxe table requires 10 minutes of sanding, 6minutes of staining, and 9 minutes of varnishing.

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Linear Programming



• A deluxe table requires 10 minutes of sanding, 6minutes of staining, and 9 minutes of varnishing.

• The profit is $3 on each standard table and $5 foreach deluxe table.

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Linear Programming Contin-ued

• Employees who do the anding and varnishingeach work at most 450 minutes per day.

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• Employees who do the anding and varnishingeach work at most 480 minute per day.

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• How many tables of each type maximizes theplant’s profit?

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• How many tables of each type maximizes theplant’s profit?

• Answer: 40 standard, 10 deluxe

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Buying a Car

You wish to by a Dodge Neon for $12,500.

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Buying a Car

You wish to by a Dodge Neon for $12,500.The car dealer offer two mutually exclusive deals: (1)a thousand dollars cash back or (2) low 1.9% interest.

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Buying a Car

You wish to by a Dodge Neon for $12,500.The car dealer offer two mutually exclusive deals: (1)a thousand dollars cash back or (2) low 1.9% interest.Which is the better deal?

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Buying a Car


• Apply the promotional $1000 to the bill andfinance the remainder of the loan from the bank at8% interest for three years.

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Buying a Car



• Finance the entire balance at the low promotionalrate of 1.9% interest for three years.

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Buying a Car



• Finance the entire balance at the low promotionalrate of 1.9% interest for three years.

• Answer: The lower interest is slightly better.

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Sets• A set is a collection of objects.

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• The terms “set,” “collection,” and “family” aresynonymous.

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• If A is a set, then “x ∈ A” means that x is anelement (or member of A, or that x belongs to A).

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• The notation x 6∈ A indicates x is not an elementof A.

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• The notation x 6∈ A indicates x is not an elementof A.

• Sets A and B are equal, A = B, if and only ifthey have the same elements.

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Set Notation• Curly braces are used for set description.

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• Sets may be specified by listing,

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• for example {1, 2, 3}, {1, 2, 3, . . . }.

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• for example {1, 2, 3}, {1, 2, 3, . . . }.

• If P (x) is a proposition about x, {x : P (x)} isthe set of exactly those x for which P (x) is true.

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• for example {1, 2, 3}, {1, 2, 3, . . . }.


• for example {x : x is a positive integer}.

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• for example {1, 2, 3}, {1, 2, 3, . . . }.


• for example {x : x is a positive integer}.

• The empty set is denoted by ∅.

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Subset• A set A is a subset of a set B if and only if each

element of A is also an element of B.

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• A ⊆ B means that A is a subset of B.

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• {a, c} ⊆ {a, b, c, d}

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• {a, c} ⊆ {a, b, c, d}

• the set of even integers is a subset of the set ofintegers

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• {a, c} ⊆ {a, b, c, d}


• the set of primes is not a subset of the set of oddintegers

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• {a, c} ⊆ {a, b, c, d}


• the set of primes is not a subset of the set of oddintegers Why not?

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Unions• Unions of sets are indicated by “∪.”

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• Thus A ∪ B and A ∪ B ∪ C denote unions.

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• A ∪B is the set of elements belonging to eitherset A, set B, or both.

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• {a, c} ∪ {b, c} = {a, b, c}

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• {a, c} ∪ {b, c} = {a, b, c}

• the set of even integers ∪ the set of odd integersis the set of integers

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Intersections• Intersections of sets are indicated by “∩,” with

usage analogous to those for “∪.”

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• A ∩B is the set of elements belonging to both setA and set B.

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• {a, c} ∩ {b, c} = {b}

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• {a, c} ∩ {b, c} = {b}

• the set of even integers ∩ the set of odd integersis ∅

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Complements

• Frequently one speaks of complements of sets.

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Complements


• Let U be the universal set for discussion.

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Complements



• If A ⊆ U is a set, thenAc = {x : x ∈ U and x 6∈ A}.

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Complements




• Ac is called the complement of A (relative to theuniversal set U ).

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Complements





• If U = {a, b, c, d, e}, then {a, c}c = {b, d, e}

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Complements





• If U = {a, b, c, d, e}, then {a, c}c = {b, d, e}

• If U is the set of integers, then the complement ofthe set of odd interers is the set of even integers.

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) =

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) = 4

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) = 4 If A = {n : n is an odd positiveinteger le30}, then n(A) =

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) = 4 If A = {n : n is an odd positiveinteger le30}, then n(A) = 15

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) = 4 If A = {n : n is an odd positiveinteger le30}, then n(A) = 15If P is the set of presidents of the United States, thenn(P ) =

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) = 4 If A = {n : n is an odd positiveinteger le30}, then n(A) = 15If P is the set of presidents of the United States, thenn(P ) = 43

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Size of a SetIf A is a set, then n(A) denotes the number ofelements in set A.n({2, 3, 5, 7}) = 4 If A = {n : n is an odd positiveinteger le30}, then n(A) = 15If P is the set of presidents of the United States, thenn(P ) = 43Even though Barack Obama is the 44th president, thecount is 43, because Grover Cleveland was elected fortwo non-consecutive terms.

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Lawyers and Liars

• There are 100 people at a meeting.

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Lawyers and Liars


• Forty are liars.

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Lawyers and Liars



• Twenty-five are lawyers.

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Lawyers and Liars




• If A is the set of liars and B is the set of lawyers,then

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Lawyers and Liars





• n(A) = 40

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Lawyers and Liars





• n(A) = 40• n(B) = 25

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Lawyers and Liars





• n(A) = 40• n(B) = 25• What’s n(A ∪B)?

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Lawyers and Liars





• n(A) = 40• n(B) = 25• What’s n(A ∪B)?• Answer: it depends on how many of the

lawyers are also liars.

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Lawyers and Liars





• n(A) = 40• n(B) = 25• What’s n(A ∪B)?• Answer: it depends on how many of the

lawyers are also liars. Isn’t that all of them?

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Picture of Graph

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Picture of Graph

liars lawyers

both

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Picture of Graph

liars lawyers

both25 10

15

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