PPT-Lecture 3 Operations on Sets

CSCI 1900 Mathematics for Computer Science Fall 2014 Bill Pine CSCI 1900 Lecture 3 2 Lecture Introduction Reading Rosen Section 22 Basic set operations Union Intersection Complement Symmetric Difference. f called regressors or basis functions data or measurements g 1 m where and usually problem 64257nd coe64259cients x so that i 1 m ie 64257nd linear combination of functions that 64257ts data leastsquares 64257t choose to minimize tot 1 All figures are courtesy of Athena Scientific and are used with permission brPage 2br SOME MATH CONVENTIONS All of our work is done in space of tuples x All vectors are assumed column vectors denotes transpose so we use to denote a row vector is Intersection. Relative Complement. Absolute Complement. Set Operations. Likened to Logical Or and Logical And. Likened to logical Negation. The . union . of two sets is the set that contains elements belonging to either of the two sets. Union. Definition. : The . union. of sets . A. and . B. , denoted by . A. . ∪ . B,. . contains those elements that are in . A. or . B. or both:. Example. : {. 1, 2, 3} . ∪ {3, 4, 5}. . = {. Sets. 2.2 Set Operations. Set Operations. Venn Diagrams. Set Identities. Union and Intersection of Indexed Collections. 2.3 Functions. 2.4 Sequences and Summations. P. 1. 1. Propositional calculus and set theory are both instances of. Dr. Andrew Wallace PhD . BEng. (hons) . EurIng. andrew.wallace@cs.umu.se. Overview. Sets. Implementation. Complexity. Graphs. Constructing . Graphs. Graph examples. Sets. Collection of items. No specified ordered. CMPS 2433- Chapter 2. Partially borrowed from Florida State . University and . Dr.. R Halverson. Introduction. A . set. is a collection of objects. The order of the elements does not matter. Objects in a set are called . S is the smallest set that contains some set I of initial elements and is closed for some operations. . Two methods to construct S:. Method I. . S is the intersection of . all . sets. . that contain I and are closed for the . Abby . yinger. Definitions. Set – any well defined collection of objects. An object in a set is called an element or member of that set. .. Crisp Sets – these are sets that only have values of 0 (‘False’) and 1 (‘True’).. Sec 2-1 . Lecture on Intro to Sets . A . set. is a collection of objects.. MATH 110 . Sec 2-1 . Lecture on Intro to Sets . A . set. is a collection of objects.. For example: . the set of seasons . S. http://. www.robots.ox.ac.uk. /~oval/. Slides available online http://. mpawankumar.info. Convex Sets. Convex Functions. Convex Program. Outline. Convex Set. x. 1. x. 2. λ. . x. 1. (1 - . λ. ) . Presented by: Andrew F. Conn. Adapted from: Adam J. Lee. Lecture #7: Introduction to Set Theory. September 20. th. , 2016. Announcements. HW #2 is out. It’s . due Monday . 10/2.. I will be out of town Monday, Dr. Ramirez will be present in my absence.. Lecture 5. Announcements!. PS1 due at midnight! . Please go over Piazza for hints. . We . will post solutions tomorrow. Grades coming soon!. Project part 1 out today!. Piazza competition! Thanks everyone for the amazing discussions!. We will first introduce set theory before we do counting.. Basic Definitions. Operations on Sets. Set Identities. Russell’s Paradox. Defining Sets. We can define a set by directly listing all its elements..