PPT-Equivalence Relations:

Selected Exercises Copyright Peter Cappello 2 Equivalence Relation Let E be a relation on set A E is an equivalence relation if amp only if it is Reflexive Symmetric Transitive. 1 Introduction We study an equivalence relation arising from a substitution tiling system in The dynamics of substitution tiling systems have been studied by many authors see KP and the references given there A tiling in gives rise to an action o Selected Exercises. Copyright © Peter Cappello. 2. Equivalence Relation. Let E be a relation on set A.. E is an . equivalence relation. . if & only if . it is:. Reflexive. Symmetric. Transitive.. Chapter 9. Chapter Summary. Relations and Their Properties. n. -. ary. Relations and Their Applications (. not currently included in overheads. ). Representing Relations. Closures of Relations (. not currently included in overheads. Chapter 9. Relations and Their Properties. Section 9.1. Binary Relations. Definition:. A . binary relation R. from a set . A. to a set . B. is a subset . R . ⊆. A . ×. B.. Example. :. Applied Discrete Mathematics Week 11: Graphs. 1. Closures of Relations . Due to the one-to-one correspondence between graphs and relations, we can transfer the definition of path from graphs to relations:. Dr. Cynthia Bailey Lee. Dr. . Shachar. Lovett. .  .                          . Peer Instruction in Discrete Mathematics by . Cynthia . Lee. is. licensed under a . Creative Commons Attribution-. Chapter 9. Chapter Summary. Relations and Their Properties. n. -. ary. Relations and Their Applications (. not currently included in overheads. ). Representing Relations. Closures of Relations (. not currently included in overheads. Applied Discrete Mathematics Week 12: Equivalence Relations. 1. Representing Relations Using Digraphs. Definition:. A . directed graph. , or . digraph. , consists of a set V of . Relations. Spring. 2015. Sukumar Ghosh. What is a relation?. Let A, B be two sets. A . binary relation . R is a subset of A X B.. Example. Let A = {Alice, Bob, Claire, Dan) be a set students,. and B= {CS101, CS201, CS202) be a set of courses. Then,. Relations and Their Properties. n. -. ary. Relations and Their Applications (. not currently included in overheads. ). Representing Relations. Closures of Relations (. not currently included in overheads. Relations. Fall. 2014. Sukumar Ghosh. What is a relation?. Let A, B be two sets. A . binary relation . R is a subset of A X B.. Example. Let A = {Alice, Bob, Claire, Dan) be a set students,. and B= {CS101, CS201, CS202) be a set of courses. Then,. CSCI 115. §4. .1. Product Sets and Partitions. §4. .1 – Product Sets and Partitions. Product Set. Ordered pair. Cartesian Product. Theorem 4.1.1. For any 2 finite non-empty sets A and B, . |A x B| = |A||B|. have been taken from the sites. http://cse.unl.edu/~choueiry/S13-235. /. and. http://. www.math-cs.gordon.edu. /courses/mat231/. notes.html. Outline. Relations. Properties of relations. Equivalence relations. Posets. (6.5). Definition: A set A (domain) together with a partial order relation R is called a partial ordered set or . poset. and is denoted by (A,R).. Example: Suppose R is the relation `divides’. We can show that (N, R) ((N,|)) is a .