Ling 310, adapted from umass ling 409, partee lecture notes march 1, 2006 p. Sets, relations, functions this note covers the following topics. Sets are welldetermined collections that are completely characterized by their elements. A binary relation from a to b is a subset of a cartesian product a x b. Relations and functions 3 definition 4 a relation r in a set a is said to be an equivalence relation if r is reflexive, symmetric and transitive. Set theory for computer science university of cambridge. Sets, relations and functions, sequences, sums, cardinality of sets richard mayr. Special types of relations are called as functions.
Set theoryrelations and functions wikibooks, open books. This module gives the learner a first impression of what discrete mathematics is about, and in which ways its flavor differs from other fields of mathematics. For those of you new to abstract mathematics elementary does not mean simple though much of the material. Sets, functions, relations northwestern university. Practically in every day of our lives, we pair the members of two sets of numbers. The video helps in understanding the concept of relations in set theory. Set, relations and functions solved examples askiitians. For example, the position of a planet is a function of time. Relations and functions are the set operations that help to trace the relationship between the elements of two or more distinct sets or between the elements of the same set. Sets, relations and functions all three are interlinked topics.
Here are three simple statements about sets and functions. Sets a set is an unordered collection of objects, e. Simple java classes implementing basic concepts of relations as defined in. Finally, we shall learn about special relations called functions. Social contract theory in moral and political philosophy, the social contract is a theory or model, originating during the age of enlightenment, that typically addresses the questions of the origin of society and the legitimacy of the authority of the state over the individual. Ling 310, adapted from umass ling 409, partee lecture notes. Sets, relations, functions introduction basic objects. We assume the reader is familiar with elementary set theory as it is used in mathematics today. Example 2 let t be the set of all triangles in a plane with r a relation in t given by r t 1, t 2. A relation refers to a set of inputs and outputs that are related to each other in some way.
Instead we follow a more conservative approach by rst choosing an appropriate set in each case on which the respective analysis is based. Relations and functions are two different words having different meaning mathematically. Sets, relations, functions questions and answers topic. Basic concepts of set theory, functions and relations 1.
The first part is aimed at helping you develop a thorough understanding of set theory and the language used in this branch of mathematics. For any two sets x and y, either there is a onetoone function from. In set theory, the concept set is extensional as oppose to intensional, namely, we dont bother about the ways in which the members of a set are chosen. Typical examples are functions from integers to integers or from the real numbers to real numbers functions were originally the idealization of how a varying quantity depends on another quantity. Georg cantor this chapter introduces set theory, mathematical induction, and formalizes the notion of mathematical functions. What is the difference between relation and function. Sub ets of a of r l numbers especially intervals with notations. Thus, two sets are equal if and only if they have exactly the same elements. Solve problems relating to sets, functions and relations. Discrete mathset theory, relations, functions and mathematical induction. Richard mayr university of edinburgh, uk discrete mathematics.
Description this is about preliminary treatment of set theory and relations, equivalence relation and binary operations meant for cbse, icse, chse and various state boards council courses in india or equivalent courses abroad. Set theory basic set theory stanford encyclopedia of. In other words, when each input in relation gets precisely one output, we refer to the relation as function. In other words, a function f is a relation such that no two pairs in the relation has the same first element. Read online basic concepts of set theory, functions and relations book pdf free download link book now.
But, before we move on to further explore the topic it is important to get the idea about the c artesian product and venn diagrams. They look like they could appear on a homework assignment in an undergraduate course. The familiar correspondence between logic and set theory leads us to the official definition. Relation from a set a to a set b is the subset of the cartesian product of a and b i. Let r be a relation from a to b and s a relation from b to c. Jun and park discussed the applications of soft sets in an ideal theory of bckbcialgebras. While we know that many will use the digital versions of the book, we encourage you to buy a paperback copy as.
Mathematics class xi sets, relations and functions unit 1. R tle a x b means r is a set of ordered pairs of the form a,b where a a and b b. Set theory, relations, and functions i 1set theory 1. Sets denote the collection of ordered elements whereas relations and functions defines the operations performed on sets the relations defines the connection between the two given sets. Instead, we will use what is callednaive set theory.
Nowadays set theory has become basic to most of the concepts in mathematics. A set is a collection of objects, called elements of the set. Java classes implementing set theory relation concepts. The basic relation in set theory is that of elementhood, or membership. Basic concepts of set theory, functions and relations. Download basic concepts of set theory, functions and relations book pdf free download link or read online here in pdf.
A set is an abstract collection of distinct objects. We write \a\in a\ to indicate that the object \a\ is an. This paper is an attempt to open up the theoretical aspects of soft. It introduces basic objects like sets, relations, functions, which form the foundation of discrete mathematics. Lecture notes on relations and functions contents 1. Basic set theory a set is a many that allows itself to be thought of as a one. Relations, functions and cartesian product set theory.
Although elementary set theory is wellknown and straightforward, the modern subject, axiomatic set theory, is both conceptually more di. Because the fundamentals of set theory are known to all mathematicians, basic problems in the subject seem elementary. By the end of this course, you will be able to define a set and represent the same in different forms. Sets, relations, functions questions and answers mathematics topic wise question bank for jee and other engineering entrance exams. Relations and functions concepts and formulae key concepts 1. In our everyday life we come across different types of relations between the. Set, relations and functions solved examples download iit jee solved examples on set, relations and functions to read more, buy study materials of set relations and functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Sets, logic, relations, and functions andrew kay september 28, 2014 abstract this is an introductory text, not a comprehensive study. A set can be represented by listing its elements between braces. Relations page 4 of 35 35 before continuing, we note that the following notation is also common in the literature. If a, b belongs to r, then a is related to b, and written as a r b if a. Free practice questions for set theory relations, functions and cartesian product. Relations and its types concepts are one of the important topics of set theory. In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set.