'Binary relation' diaporamas de présentation

Chapter 8

Chapter 8. Relations. Contents. 1. Relations and their properties 2. n-ary relations and their applications 3. Representing relations 4. Closure of relations 5. Equivalence relations 6. Partial orderings. 8.1 Relations and their properties. Def. 1: A, B: two sets.

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Discrete Structure

Discrete Structure. Li Tak Sing( ??? ). From grammar to inductive definition. Consider the following grammar: S ??|aB B ?b|bB Basis: ?, ab?L(G) Induction: if ay ? L(G), then aby ? L(G). Constructing grammars. {a n |n ?N} S??|aS {a n b n |n ?N} S ??|aSb {(ab) n |n?N} S ??|abS.

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Chap. 7 Relations: The Second Time Around

Chap. 7 Relations: The Second Time Around. Binary Relation. For sets A, B, any subset of A ? B is called a (binary) relation from A to B. Any subset of A ? A is called a (binary) relation on A. Reflexive Relation. e.g. Given a finite set A with |A|=n. Then,

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Rough Sets

Rough Sets. Basic Concepts of Rough Sets. Information/Decision Systems (Tables) Indiscernibility Set Approximation Reducts and Core Rough Membership Dependency of Attributes. IS is a pair ( U, A ) U is a non-empty finite set of objects.

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Decision Theory Preference relation and choice function

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Discrete Mathematics

Discrete Mathematics. 3. MATRICES, RELATIONS, AND FUNCTIONS. Lecture 5. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. Homework 4. Prove that for arbitrary sets A and B , the following set equation apply: a) A ? ( A ? B ) = A ? B b) A ? ( A ? B ) = A ? B.

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Relations (1)

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L ogics for D ata and K nowledge R epresentation

L ogics for D ata and K nowledge R epresentation. Modal Logic. Originally by Alessandro Agostini and Fausto Giunchiglia Modified by Fausto Giunchiglia, Rui Zhang and Vincenzo Maltese. Outline. Introduction Syntax Semantics Satisfiability and Validity Kinds of frames

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CS322

Week 8 - Wednesday. CS322. Last time. What did we talk about last time? Cardinality Countability Relations. Questions?. Logical warmup. There is a Grand Hotel with an infinite number of rooms Their slogan is: "We're always full, but we always have room for you!"

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MT263F Discrete Structures

MT263F Discrete Structures. Li Tak Sing ( ??? ). Functions. If A and B are sets and so that each element in A is associated with exactly one element in B. Such association is called a function from A to B.

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Axiomatic set theory

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Section 7.1

Section 7.1. Relations and their properties. Binary relation. A binary relation is a set of ordered pairs that expresses a relationship between elements of 2 sets Formal definition: Let A and B be sets A binary relation from A to B is a subset of AxB (Cartesian product).

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Discrete Structure

Discrete Structure. Li Tak Sing( ??? ). Chapter 4 Properties of Binary Relations. Three special properties For a binary relation R on a set A, we have the following definitions. R is reflexive if xRx for all x ?A. R is symmetric if xRy implies yRx for all x,y ?A

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CSPs and Relational DBs Foundations of Constraint Processing CSCE421/821, Fall 2005:

CSPs and Relational DBs Foundations of Constraint Processing CSCE421/821, Fall 2005: www.cse.unl.edu/~choueiry/F05-421-821/ Berthe Y. Choueiry (Shu-we-ri) Avery Hall, Room 123B choueiry@cse.unl.edu Tel: +1(402)472-5444. Background.

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8.3 Representing Relations

8.3 Representing Relations . Connection Matrices Let R be a relation from A = { a 1 , a 2 , . . . , a m } to B = {b 1 , b 2 , . . . , b n }. Definition: A n m ? n connection matrix M for R is defined by M ij = 1 if <a i , b j > is in R, = 0 otherwise.

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Relations and Their Properties

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Discrete Mathematics by Meri Dedania Assistant Professor MCA department

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Relations

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Digraphs and Relations Warm Up

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