set theory lecture notes ppt

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A set A is said to be subset of another set B if and only if every element of set A is also a part of other set B. Denoted by ‘⊆‘. Basics. Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. PPT ON PROBABILITY THEORY &STOCHASTIC PROCESS II B.Tech I semester (JNTUH-R15) Prepared by Ms.G.Mary Swarna Latha (Assistant professor) Mr.G.Anil kumar reddy (Assistant professor) probability introduced through sets and relative frequency • Experiment:- a random experiment is an action or process that leads to one of several possible outcomes Experiment Outcomes Flip a coin Heads, Tails … Introduction to Sets Countdown Class 4 Third Edition Chapter # 1 Solution Word Problems 2, Countdown Class 4 Third Edition Chapter # 1 Solution Word Problems, Countdown Class 4 Third Edition Chapter # 2 Solution, Countdown Class 4 Third Edition Chapter # 1 Solution, No public clipboards found for this slide, Introduction to Sets Theory in Mathematics, Attended comsats institute of information and technology, Fatima Jinnah Women University Rawalpindi. CONTENTS 5 Preface These notes for a graduate course in set theory are on their way to be- coming a book. Each p. cm. Cynthia Church pro- duced the first electronic copy in December 2002. A book of set theory / Charles C Pinter. “A revised and corrected republication of Set Theory, originally published in 1971 by Addison-Wesley Publishing Company, Reading, Massachusetts.” Summary: “This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. (iii) The set of real numbers between ‘1’ and ‘2’. 1. •The set of months is a finite set because it has 12 elements. BASIC CONCEPTS OF SETS Content Define a set Represent a set Define the number of elements of a set Practice Problems 1 Compare sets Recognize different types of set Practice Problems 2 Define the subsets of a set Review Exercises 1 OPERATIONS ON SETS Determine the union of two or more sets Practice Problems 3 Determine the intersection of two or more sets Practice Problems 4 Determine the complement of a set Determine the difference of two sets Practice Problems … See our Privacy Policy and User Agreement for details. 6. De ning a set formally is a pretty delicate matter, for now, we will be happy to consider an intuitive de nition, namely: De nition 24. My Email Address ± The set of even prime numbers is a finite set. If you continue browsing the site, you agree to the use of cookies on this website. An art collector might own a collection of paintings, while a music lover might keep a collection of CDs. (ii) The set of all natural numbers. These notes were prepared using notes from the course taught by Uri Avraham, Assaf Hasson, and of course, Matti Rubin. NB (Note Bene) - It is almost never necessary in a mathematical proof to remember that a function is literally a set of ordered pairs. De nition 1.8 (Injection). Learn more. Set. The Note: | | = 0 Power Set power set P(S) of a given set S is the set of all subsets of S: P(S) = { A | A S}. Set Theory \A set is a Many that allows itself to be thought of as a One." Looks like you’ve clipped this slide to already. Now customize the name of a clipboard to store your clips. ± The set of positive integers is an infinite set. 1.The empty set, denoted ?, is the set that has no element. The predicate P(n) de ned on the set of natural numbers by \nis even" takes the following values upon evaluation on n: P(0) = 1, P(1) = 0, P(2) = 1, P(3) = 0, etc. Subset. Example ± For S= {1,2,3} As of this date, Scribd will manage your SlideShare account and any content you may have on SlideShare, and Scribd's General Terms of Use and Privacy Policy will apply. Introduction to Sets Basic Set Theory The following notations will be followed throughout the book. Subject: Mathematics Set Partition Definition. They originated as handwritten notes in a course at the University of Toronto given by Prof. William Weiss. Infinite set: A set which is not a finite set, i.e., a set consisting of infinite number of elements is called an infinite set. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. ‘A ⊆ B ‘ denotes A is a subset of B. We can use these sets understand relationships between groups, and to analyze survey data. Note that empty list notation {} is not usually used for the empty set, we have a … 2. Set Theory. Ling 409, Partee lecture notes, Lecture 1 September 7, 2005 p. 4 From the definition of identity follows that there exists only one empty set; its identity is fully determined by its absence of members. Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 3 Set Theory Basics.doc Predicate notation. ± The set of prime numbers is an infinite set. Basic and Advanced Defining a Set • The symbol ‘∈’ is used to denote belongs to or is an element of or is a member of set. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. When we “partition a set,” we break it down into mutually exclusive and exhaustive regions, i.e., regions with no overlap. Edition of August 9, 2017: chapter on proper forcing rewritten. Concepts We say that a group of sets partitions another set if they are mutually exclusive and exhaustive with respect to that set. It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. Preface Edition of March 11, 2019: chapter on p = t rewritten. Any collection of items can form a set. Z:= f0;1; 1;2; 2;:::g, the set of Integers; 5. Lecture Slides By Adil Aslam. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. James Talmage Adams produced the copy here in February 2005. If you wish to opt out, please close your SlideShare account. •a A “a is an element of set A” “a is a member of set A” •a A “a is not an element of set A” • Order of elements is meaningless. See our User Agreement and Privacy Policy. You can change your ad preferences anytime. (Georg Cantor) In the previous chapters, we have often encountered "sets", for example, prime numbers form a set, domains in predicate logic form sets as well. LECTURES ON SET THEORY J. Donald Monk March 11, 2019 i. Q:= fp q: p;q2Z;q6= 0 … Clipping is a handy way to collect important slides you want to go back to later. … Introduction to Sets Lecture Slides By Adil Aslam. N:= f1;2;:::g, the set of Natural numbers; 3. To prove A is the subset of B, we need to simply show that if x belongs to A then x also belongs to B. They are not guaran-teed to be comprehensive of the material covered in the course. These lecture notes were prepared with the purpose of helping the students to follow the lectures more easily and e ciently. W:= f0;1;2;:::g, the set of whole numbers 4. Edition of November 14, 2016: chapter on proper forcing changed; the proof of The-orem 28.5 was in error, and a new proof using a game is given (Theorem 28.33). This course is a fast-paced course (like many courses in the depart- ment) with a signi cant amount of material, and to cover all of this material at a reasonable pace in the lectures, we intend to bene t from these partially-complete lecture notes. Example: {x x is a natural number and x < 8} Reading: “the set of all x such that x is a natural number and is less than 8” So the second part of this notation is a prope rty the members of the set share (a condition Scribd will begin operating the SlideShare business on December 1, 2020 Defining a Set Examples of Set Numerical Sets (Well-Defined) Representation of a Set Famous Sets in Math Finite and infinite Sets Empty Set / Null Set Singleton Set or Unit Set Equal and Equivalent Sets Cardinality of Sets Subsets Power Sets Disjoint Sets Union of Sets Intersection of Sets Complement of a Set. NOTE: Order of elements of a set doesn’t matter. Eg: (i) The set of all straight line in a given plane. The binary predicate R(a;b) de ned on the set of real number by \ais smaller than b" is true for a= 0 and b= 1 and false for a= 4 and b= 2.

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