Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Set theory if we are interested in elements of a set a that are not contained in a set b, we can write this set as a. It is a very basic and easy concept but has significant use in algebra, logic, combinatorics, probability etc. This cheat sheet covers the high school math concept set theory. A little set theory never hurt anybody matthew saltzman department of mathematical sciences clemson university draft. With setbuilder notation, we can list a few more very important sets. A set is a collection of items that share something in common, e. Refer to the diagram to answer the questions below. Solved examples to find intersection of two given sets. A fun activity that can be done individually, in peers or groups. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions.
The shaded parts of the diagrams are the intersections and unions respectively. The cardinality of the union and intersection of the sets a and b are. March 30, 2009 basic set theory we will use the standard notation for containments. It sounds simple, but set theory is one of the basic building blocks for higher mathematics, so it helps to understand the basics well. Bread a intersection b or the intersection of a and bis defined as the set composed of all elements that belong to both a and b. A set is pure if all of its members are sets, all members of its members are sets, and so on. This chapter introduces set theory, mathematical in duction. Introduction to intersection theory in algebraic geometry lectures. Video for all operations of sets extra practiceinteractive links.
What set notation would you use to represent the following regions. This region is called the intersection of the two sets. Get 100% clarification of set theory, subset, union, intersection and venn diagram with pdf. Intersection, is only where the two sets intersect, or overlap. This page sets out the principles of sets, and the elements within them. Students will cut and paste appropriate solutions to seven 7 questions on set theory involving union, intersection and complement.
Such as, sets could be a collection of odd numbers, even numbers, natural numbers, whole numbers, real or complex numbers and all the set of numbers which comes in the number line. Not to be confused with intersectionality theory in mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring. Finally, since we are trying to shade the intersection, in this last step we finish our diagram by shading only the overlap from the previous image. The intersection operation is denoted by the symbol the set a. Here are some examples of set operations and their venn diagrams. Some intersection theorems for ordered sets and graphs.
The intersection of a and b, denoted by a b, is the set that contains those elements that are in both a and b. The intersection of two sets is the set consisting of those elements that. These elements could be numbers, alphabets, variables, etc. Given three sets a, b, and c the intersection is the set that contains elements or objects that belong to a, b, and to c at the same time. Let us see the different types of symbols used in mathematics set theory with its meaning and examples. Set theory concept of subset, union and intersection pdf. By appointment, in 380383m third floor of the math building. A solved problem based on union and intersection of. Introduction to logic and set theory 202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Basic concepts of set theory, functions and relations.
The word set and other similar words are frequently used in our daily lifes vocabulary, such as a set of cards, a bunch of keys, a pack of cigarette and so on. In this section we define the power set and give some examples. In all the examples, the intersection is a subset of each set forming the intersection. In mathematics, a set is a collection of different or distinct objects.
It assumes no knowledge of logic, and no knowledge of set theory beyond the vague familiarity with curly brackets, union and intersection usually expected of an advanced mathematics. In mathematics, the intersection of two sets a and b, denoted by a. Set theory and logic supplementary materials math 103. These notes were prepared using notes from the course taught by uri avraham, assaf hasson, and of course, matti rubin. From the earliest times, mathematicians have been led to consider sets of objects of one kind or another, and the elementary notions of modern set theory are.
The notation and symbols for sets are based on the operations performed on them. A set is a collection of objects, nothing more and nothing less. Pdf on apr 7, 2016, kawther abbood neamah and others published. The set operation intersection takes only the elements that are in both sets. An introduction to elementary set theory guram bezhanishvili and eachan landreth 1 introduction in this project we will learn elementary set theory from the original historical sources by two key gures in the development of set theory, georg cantor 18451918 and richard dedekind 18311916. Associative law states that the grouping of set operation does not change the result of next grouping of sets. In maths, set theory was developed to explain about collections of objects. It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. Find materials for this course in the pages linked along the left.
This series of lessons cover the essential concepts of math set theory the basic ways of describing sets, use of set notation, finite sets, infinite sets, empty sets, subsets, universal sets, complement of a set, basic set operations including intersection and union of sets, using venn diagrams and simple applications of sets. Video for interval notation set builder notationroster notation 2. Set theory is a branch of mathematics that studies sets. Basic set theory a set is a many that allows itself to be thought of as a one. For example, a deck of cards, every student enrolled in. Set theory is a branch of mathematics which deals with the study of sets or the collection of similar objects. Although a comprehensive history of this vast subject is not attempted, the author points out some of the striking early appearances of the ideas of intersection theory. And if you do learn set theory you most likely wont recognize that you are even.
A set cannot have the same member twice never more than once. Set is the definite collection of welldefined objects is called set. For example, the set containing only the empty set is a nonempty pure set. Usually we denote sets with uppercase letters, elements with lowercase letters. Here are some useful rules and definitions for working with sets. A roster is a list of the elements in a set, separated by commas and surrounded by french curly braces. Iournal of combinatorial theory, series a 43, 2337 1986 some intersection theorems for ordered sets and graphs f. I offer no definition of what a set is beyond the intuitive notion described above. Although elementary set theory is wellknown and straightforward, the modern subject, axiomatic set theory, is both conceptually more di. The following notation is used to show set membership means that x is a member of the set a means that x is not a member of the set a. It is designed for a onesemester course in set theory at the advanced undergraduate or beginning graduate level. The notion of set is taken as undefined, primitive, or basic, so we dont try to define what a set is, but we can give an informal description, describe important properties of sets, and give examples. The notion of set is taken as undefined, primitive, or basic, so we dont try to define what a set is, but we can give an informal description, describe.
P 1 which can also be interpreted as the nonsingular quadric q in p 3 has selfintersection 0, since a line can be moved off itself. Ling 310, adapted from umass ling 409, partee lecture notes march 1, 2006 p. The union, intersection, difference and complement of sets can be depicted graphically by means of venn diagrams. 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. Some new operations in soft set theory we point out here that the intersection of two soft sets introduced in 2 see definition 1.
But even more, set theory is the milieu in which mathematics takes place today. The intersection of two sets contains only the elements that are in both sets. Georg cantor this chapter introduces set theory, mathematical in duction, and formalizes the notion of mathematical functions. Introduction to logic and set theory202014 general course notes december 2, 20 these notes were prepared as an aid to the student.
Definition of intersection of sets some properties of operation of. One says that the affine plane does not have a good intersection theory, and intersection theory on nonprojective varieties is much more difficult. Set symbols of set theory and probability with name and definition. Basically, the definition states it is a collection of elements. Foundations of mathematics i set theory only a draft. They are not guaranteed to be comprehensive of the material covered in the course. Basics of set theory with venn diagrams handa ka funda. Intersection of sets minnesota state university moorhead. Complex issues arise in set theory more than any other area of pure mathematics. Each set is shown as a circle and circles overlap if the sets intersect. For those of you new to abstract mathematics elementary does not mean simple though much of the material. August 19, 2019 1 introduction the fundamental ideas of set theory and the algebra of sets are probably the most important concepts across all areas of mathematics other than the algebra of real numbers.
The complement of a set a contains everything that is not in the set a. Chapter 4 set theory \a set is a many that allows itself to be thought of as a one. So the intersection of the empty family should be the universal set the identity element for the operation of intersection unfortunately, according to standard set theory, the universal set does not exist. A fix for this problem can be found if we note that the intersection over a set of sets is always a subset of the union over that set of sets. These sets are examples of some of the most common set operations, which are. Instead, i am going to show you what can be done with sets. Set theory empty set the set that contains no element is called the empty set or null set. Review of set theory michael williams last updated. Set simple english wikipedia, the free encyclopedia.
Aug 08, 2014 a solved problem based on union and intersection of set theory. This alone assures the subject of a place prominent in human culture. Set theory is one of the most fundamental branch of mathematics, but is also also very complex if you try to analyze three or more sets. Intersection of two given sets is the largest set which. Sep 24, 2017 next, we need to find the intersection of b. A solved problem based on union and intersection of set theory.
If set x and set y have the same members, then x y. In a venn diagram the universe u is represented by points within a rectangle and sets a, b, c, etc. Nb note bene it is almost never necessary in a mathematical proof to remember that a function is literally a set of ordered pairs. Thus, the intersection of the two committees read more. Media in category intersection set theory the following 22 files are in this category, out of 22 total. Set theory is a very important branch of mathematics that has wide ranging applications. We will refrain from giving non mathematical examples such as the set of pupils in. Are you getting confused in the set theory concept. The aim of this book is to develop the foundations of this theory, and to indicate the range of classical and modern applications. B for example, if s is the set of all juices in the supermarket, and t is the set of all. The notation represents the entire region covered by both sets a and b and the section where they overlap. Set theory was developed by german mathematician georg cantor in the second half of the nineteenth century.
298 225 1127 1477 886 1067 725 932 835 1001 529 1011 819 1158 315 922 642 385 1449 1246 1097 1513 1232 231 671 714 1474 761 464 1034 108 27 809 9 884 378 1301 344 746 196 709 699 977 1363