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Sets, Functions, Relations - Northwestern...

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Sets, Functions, Relations - Northwestern...

CHAPTER 2 Sets, Functions, Relations 2.1. Set Theory 2.1.1. Sets. A set is a collection of objects, called elements of the set. A set can be represented by listing ...

http://www.math.northwestern.edu/%7Emlerma/courses/cs310-05s/notes/dm-sets.pdf

Date added: August 19, 2016 - Views: 1

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01 - Sets, Relations and Functions

01 - SETS, RELATIONS AND FUNCTIONS Page 2 ( Answers at the end of all questions ) ( 8 ) The domain of the function f ( x ) =

http://www.schoolnotes4u.com/Mathematics%20Objectives/01%20-%20Sets%2C%20Relations%20and%20Functions.pdf

Date added: August 18, 2016 - Views: 1

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Basic Concepts of Set Theory, Functions and...

Basic Concepts of Set Theory, Functions and Relations 1. ... Function composition ... Such a relation between sets is denoted by A ...

http://people.umass.edu/partee/NZ_2006/Set%20Theory%20Basics.pdf

Date added: August 18, 2016 - Views: 5

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Chapter 2 Sets, Relations and Functions - Springer

Chapter 2 Sets, Relations and Functions Key Topics Sets Set Operations Russell’s Paradox Relations Composition of Relations Reflexive, Symmetric and Transitive ...

http://www.springer.com/cda/content/document/cda_downloaddocument/9781447145332-c1.pdf?SGWID=0-0-45-1355802-p174596963

Date added: August 31, 2016 - Views: 1

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SETS, RELATIONS, AND FUNCTIONS - School of...

Sets Relations and functions Countability Examples Summary Sets and notations Common Universal Sets Subset and Power Set Cardinality Operations Sets I A set is a ...

http://www.computing.dcu.ie/~away/CA215/jie_w1.pdf

Date added: September 21, 2016 - Views: 1

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Discrete Mathematics, Chapters 2 and 9: Sets,...

Discrete Mathematics, Chapters 2 and 9: Sets, Relations and Functions, Sequences, Sums, Cardinality of Sets Richard Mayr University of Edinburgh, UK

http://www.inf.ed.ac.uk/teaching/courses/dmmr/slides/13-14/Ch2.pdf

Date added: August 18, 2016 - Views: 3

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01 - SETS, RELATIONS AND FUNCTIONS Page 1...

01 - SETS, RELATIONS AND FUNCTIONS Page 2 ( Answers at the end of all questions ) ( 8 ) The domain of the function f ( x ) =

https://kv1mlibarchives.files.wordpress.com/2013/07/mathematics-set-relation-function-mcq.pdf

Date added: September 21, 2016 - Views: 1

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Sets, Relations and Functions - Pacuit

Sets, Relations and Functions ... The union of two sets can be pictured as follows ... (Function) A function f is a binary relation on A and B (i.e.,

http://pacuit.org/media/courses/discretemath_2_1.pdf

Date added: September 21, 2016 - Views: 1

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Functions, Sets, and Relations - Cognitive science

A relation over sets A 1 ... right-total binary relation is sometimes called a surjective relation. Also, note that a function is surjective iff ... Sets, and Relations

http://www.cogsci.rpi.edu/~heuveb/teaching/Logic/CompLogic/Web/Handouts/SetsRelationsFunctions.pdf

Date added: September 21, 2016 - Views: 1

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Classical Analysis I 1 Sets, relations, functions

Classical Analysis I 1 Sets, relations, functions A set is considered to be a collection of objects. The objects of a set A are called elements of A.

http://www.math.psu.edu/wysocki/M403/Notes403_1.pdf

Date added: September 21, 2016 - Views: 1

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Math Class 11 Chapter 1 and 2 Sets and relations...

Math Class 11 Chapter 1 and 2 Sets and relations and functions ... Relation If A and B are two non-empty sets, then a relation R from A to B is a subset of A x B.

http://ncerthelp.com/cbse%20notes/class%2011/maths/All%20formulas%20and%20notes%20for%20maths%20class%2011%20note%20download%20Chapter%20%201%20and%202%20sets%20and%20relations%20and%20functions%20.pdf

Date added: August 18, 2016 - Views: 1

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Sets, Relations Functions and

Relation If A and B are two non-empty sets, ... Let A and B be two non-empty sets, then a function f from set Ato set B is a rule which associates each element of to a

http://www.arihantbooks.com/chapterdownloads/C134.pdf

Date added: September 21, 2016 - Views: 1

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3.1 Functions relation Example - FIU

3.1 Functions A relation is a set of ordered pairs (x, y). Example: The set {(1,a), (1, b), (2,b), (3,c), (3, a), (4,a)} is a relation A function is a relation (so ...

http://www2.fiu.edu/~wlodarcz/chapter3.pdf

Date added: August 18, 2016 - Views: 18

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1 Day Sets, Relations and Functions -...

Sets, Relations and Functions Day 1 Day 1Outlines Types of Set Power Set Operation on Sets Cartesian Product of Sets Relation Function or Mapping

http://arihantbooks.com/chapterdownloads/C144.pdf

Date added: August 20, 2016 - Views: 1

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Algebra I Notes Relations and Functions Unit 03a...

Algebra I Notes Relations and Functions Unit 03a ... determine if a given relation is a function describe and model functions using an input-output table, ...

http://www.saylor.org/site/wp-content/uploads/2014/01/K12MATH8-FLC-Unit3.1-FunctionsAndRelations.pdf

Date added: August 20, 2016 - Views: 2

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7 Relations and Functions - Arkansas Tech...

7 Relations and Functions In this section, we introduce the concept of relations and functions. Relations A relation Rfrom a set Ato a set Bis a set of ordered pairs ...

http://faculty.atu.edu/mfinan/2033/section7.pdf

Date added: August 19, 2016 - Views: 2

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Discrete Mathematics: Lectures 6 and 7 Sets,...

Discrete Mathematics: Lectures 6 and 7 Sets, Relations, Functions and Counting Instructor: Arijit Bishnu Date: August 4 and 6, 2009 Our main goal is here is to do ...

http://www.isical.ac.in/~arijit/courses/autumn2009/discrete09/lec6-dm09.pdf

Date added: August 21, 2016 - Views: 1

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Metho - Computer Science | Your Education

Sets, Relations, Functions Ivo Düntsch ... Here are some elementary properties of the ⊆ relation: Lemma 1.2.1. ∅ is a subset of every set. Proof.

http://www.cosc.brocku.ca/~duentsch/archive/methprimer1.pdf

Date added: August 18, 2016 - Views: 1

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Unit SF Sets and Functions - UCSD Mathematics

Unit SF Sets and Functions Section 1: Sets The basic concepts of sets and functions are topics covered in high school math courses

http://www.math.ucsd.edu/~ebender/DiscreteText1/SF.pdf

Date added: August 20, 2016 - Views: 1

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1 Set Theory and Functions - The University of...

1 Set Theory and Functions 1.1 Basic De–nitions and Notation A set A is a collection of objects of any kind. We write a 2 A to indicate that a is an element of A ...

http://www.unc.edu/~normanp/890part1.pdf

Date added: August 20, 2016 - Views: 1

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Class XII: Math Key Concepts - Rediff.com

Class XII: Math Chapter: Relations and Functions Concepts and Formulae Key Concepts 1. A relation R between two non empty sets A and B is a subset of their

http://im.rediff.com/getahead/2010/feb/19relations-functions-trig.pdf

Date added: September 2, 2016 - Views: 2

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Relations and Functions (Mathematics)

Relations and Functions (Mathematics) Relations ... A function is a special type of relation, whereby no x-value (abscissae) can be repeated.

http://www.nointrigue.com/docs/notes/maths/maths_relfn.pdf

Date added: August 19, 2016 - Views: 6

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N E 44..33 Identifying Functions

E x a m p l e 1 Identifying a Function For each table of values below, decide whether the relation is a function. (a) (b) (c) Part a represents a function.

http://www.mhhe.com/math/devmath/hutchison/student/olc/graphics/hutchison01eia_s/ch04/others/ch04-3.pdf

Date added: August 19, 2016 - Views: 1

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Functions between Sets - University of Hawaii...

Chapter 3 Functions between Sets 3.1 Functions 3.1.1 Functions, Domains, and Co-domains In the previous chapter, we investigated the basics of sets and operations on

http://www2.hawaii.edu/~robertop/Courses/TMP/3_Functions.pdf

Date added: September 29, 2016 - Views: 1

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1.4 Relations and Functions A relation is a...

1.4 Relations and Functions A relation is a correspondence between two sets. If x and y are two elements in these sets and if a relation exists between x and y, then x

http://web.cerritos.edu/dford/SitePages/Math_60_F08/Math_140/Math140Lecture3.pdf

Date added: September 29, 2016 - Views: 1

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Discrete Mathematics - Faculteit Wiskunde en...

Discrete Mathematics 1. Relations 1.1. Binary relations A (binary) relation R between the sets S and T is a subset of the cartesian product S ×T.

http://www.win.tue.nl/~hansc/dw/notes.pdf

Date added: August 18, 2016 - Views: 4

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CHAPTER 12 Functions - People.vcu.edu

Functions 199 If A and B are not both sets of numbers it can be difficult to draw a graph of f : A ! B in the traditional sense. Figure 12.3(a) shows an

http://www.people.vcu.edu/~rhammack/BookOfProof/Functions.pdf

Date added: August 18, 2016 - Views: 3

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Introduction Relations - CSE at UNL

Introduction Recall that a relation between elements of two sets is ... We have seen ways of graphically representing a function/relation between two (di erent) sets ...

http://cse.unl.edu/~choueiry/S06-235/files/Relations-HandoutNoNotes.pdf

Date added: August 21, 2016 - Views: 2

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Relations and Functions A.2.3 (includes A.2.13)

2 Which of the following sets of ordered pairs could ... 6 Identify the mapping diagram that represents the relation and determine whether the relation is a function.

http://cypressbayhighschool.com/?p=160&aid=176&sa=0

Date added: August 19, 2016 - Views: 5

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miL2872X ch04 255-308 9/26/06 02:15 PM Page 255 IA...

quadratic function. 3. A function whose graph is a ... Domain and Range of a Relation In many naturally occurring phenomena, two variables may be linked by some

https://people.ucsc.edu/~miglior/chapter%20pdf/Ch04_SE.pdf

Date added: August 18, 2016 - Views: 2

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Math Worksheet 1 FUNCTION versus RELATION -...

Worked out by Jakubíková K. 1 Math Worksheet 1– FUNCTION versus RELATION Relations A relation is a set of inputs and outputs, often written as ordered pairs ...

http://www.ssag.sk/files/1Relation-vs-Function-wsh1.pdf

Date added: August 19, 2016 - Views: 7

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MTH-4109-1 Sets, Relations Functions

MTH-4109-1 Sets, Relations and Functions ... Cartesian Graph of a Function ... The second part will allow you to master the concept of relation and the formal

http://www.sofad.qc.ca/media/doc/cours/307_X-1520.pdf

Date added: November 11, 2016 - Views: 1

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Relations as Functions Independent Practice...

Relations as Functions - Independent Practice Worksheet ... 1 8 1 7 Is this relation a function? 2. Look at the domain values in the table: Domain Range -19 10

http://www.mathworksheetsland.com/functions/1relations/ip.pdf

Date added: August 18, 2016 - Views: 7

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Sets and Functions - UC Davis Mathematics

2 1. Sets and Functions Sets are determined entirely by their elements. Thus, the sets X, Y are equal, written X= Y, if x2X if and only if x2Y: It is convenient to de ...

https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/ch1.pdf

Date added: August 20, 2016 - Views: 1

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3. RELATIONS AND FUNCTIONS - Macquarie University

27 3. RELATIONS AND FUNCTIONS §3.1 Relations . Having defined relations and functions as certain types of statement we redefine them within the class of sets.

http://web.science.mq.edu.au/~chris/sets/CHAP03%20Relations%20and%20Functions.pdf

Date added: November 11, 2016 - Views: 1

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Lecture # 1 (Sets, Functions and equivalence...

Lecture # 1 (Sets, Functions and equivalence Relations) MTH 232, Abstract Algebra ... Binary Relation ... Is every rule between two sets a function (or well defined).

http://www.puremaths.info/wp-content/uploads/2013/02/LEC_1_AA1.pdf

Date added: September 29, 2016 - Views: 1

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Introduction to Relations - Department of...

CHAPTER 7 Introduction to Relations 1. Relations and Their Properties 1.1. De nition of a Relation. De nition: A binary relation from a set A to a set Bis a subset

http://www.math.fsu.edu/~pkirby/mad2104/SlideShow/s7_1.pdf

Date added: August 23, 2016 - Views: 1

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Notation for Sets of Functions and Subsets -...

Notation for Sets of Functions and Subsets Recall that we de ned a sequence as a function on the domain N of natural numbers. Thus, a sequence of real numbers | i.e ...

http://www.u.arizona.edu/~mwalker/econ519/Econ519LectureNotes/SetOfAllFunctions.pdf

Date added: August 21, 2016 - Views: 1

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Binary relations and properties Relationship to...

Binary relations establish a relationship between elements of two sets Definition: Let A and B be two sets. A binary relation from A to B is a subset of A ×B.

http://www.pitt.edu/~bonidie/cs441/relations.pdf

Date added: August 20, 2016 - Views: 1

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Section 5. Relations and Functions 5.1. Cartesian...

WUCT121 Logic 179 5.2. Relations 5.2.1. Definition: Binary Relation Let A and B be sets. We say that R is a (binary) relation from A to B if R ⊆A×B.

http://www.uow.edu.au/~bmaloney/wuct121/LogicWeek10Lecture1.pdf

Date added: August 29, 2016 - Views: 1

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Contents

Contents 1. Relations 1 ... Let f: R !R be a function. Then we can de ne a relation from ... We still have not given a formal de nition of a relation between sets ...

http://math.uga.edu/~pete/3200relationsfunctions.pdf

Date added: August 20, 2016 - Views: 1

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Lecture 1. Basic Concepts of Set Theory, Functions...

Lecture 1. Basic Concepts of Set Theory, Functions and Relations 0. Preliminaries ... Such a relation between sets is denoted by A ...

http://people.umass.edu/partee/409/Lecture1%20Set%20Theory%20Sept%207.pdf

Date added: August 18, 2016 - Views: 5

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A relation is a set of ordered pairs function -...

A relation is a set of ordered pairs Every function is a relation, but not vice ... Relations Page 1 . General relations: A relation R on sets S, T is a subset of ...

http://www.cs.tufts.edu/comp/14/notes/Relations.pdf

Date added: November 11, 2016 - Views: 1

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De–ne Function, Domain, and Range

Since we will often work with sets of ordered pairs of the ... –nd the domain and range and determine whether the relation de–nes y to be a function of x. a) b) x ...

http://math.ucr.edu/~blopez/chc/presente/10fallmath102/3.1

Date added: August 20, 2016 - Views: 2

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Functions Let A and B be sets. A function...

Discrete Mathematics by Section 1.6 and Its Applications 4/E Kenneth Rosen TP 1 Section 1.6 Functions Definition: Let A and B be sets. A function (mapping,

http://www.cs.rutgers.edu/~elgammal/classes/cs205/functions_2.pdf

Date added: August 29, 2016 - Views: 1

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SETS - RELATIONS - Rankers Learning

Let R be the relation over the set of all straight lines in a plane such that ... a function 2) transitive 3) ... Sets-Relations Ranker relation 1 1 ...

http://www.rankerslearning.com/wp-content/uploads/2014/04/1.-SETS-RELATIONS.pdf

Date added: September 21, 2016 - Views: 1

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Lecture 2: functions and cardinality - Princeton...

Lecture 2: functions and cardinality Just a note from last time. If we have an equivalence relation R on a set A, it is standard notation to write

https://web.math.princeton.edu/~mdamron/teaching/F12/notes/MAT_215_Lecture_2.pdf

Date added: November 11, 2016 - Views: 1

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Relations and Functions 19.10.06 - Prashanth...

RELATIONS AND FUNCTIONS 3 Definition 4 A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive. Example 2 Let T be ...

http://ncertbooks.prashanthellina.com/class_12.Mathematics.MathematicsPartI/Relations%20and%20Functions%20ch%201.pdf

Date added: August 18, 2016 - Views: 1

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Chapter 2 Relations, Functions, Partial Functions

Chapter 2 Relations, Functions, Partial ... which is equivalent to view the function as a relation). ... Definition 2.2.1 Given two sets, A and B,a(binary) relation ...

http://www.seas.upenn.edu/~jean/cis160/cis160slides4.pdf

Date added: August 31, 2016 - Views: 1