For two distinct set, a and b with cardinalities m and n, the maximum cardinality of the relation r from a to b is mn. 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. X x 1 the collection x 1,x 2,x 3,x 4 x 2 x 4 is a partition of x x 3 theorem. Whenever sets are being discussed, the relationship between the elements of the sets is the next thing that comes up. Discrete mathematics is the branch of mathematics dealing with objects. Discrete mathematicsfunctions and relations wikibooks. These problem may be used to supplement those in the course textbook. Students are assumed to have taken comp 1805 discrete structures i, which covers mathematical reasoning, basic proof techniques, sets, functions, relations, basic graph theory, asymptotic notation, and countability. Cheat sheetstudy sheet for a discrete math class that covers sequences, recursive formulas, summation, logic, sets, power sets, functions, combinatorics, arrays and matrices. Introduction sets are one of the basic building blocks for the types of objects considered in discrete mathematics important for counting programming languages have set operations. Mar 17, 2011 topics 1 relations introduction relation properties equivalence relations 2 functions introduction pigeonhole principle recursion 93.
Examples of discrete structures built with the help of sets. A binary relation from a to b is a subset of a cartesian product a x b. Sets and set operations cs 441 discrete mathematics for cs m. A function defined on sets a,b a b assigns to each. Pigeonhole principle, inclusionexclusion principle, equivalence and partial orderings under ugc net computer science paper ii syllabus. In this if a element is present then it is represented by 1 else it is represented by 0. During a 12week term with three hours of classes per week, i cover most. Venn diagram, invented in 1880 by john venn, is a schematic diagram that shows all possible logical relations between different mathematical sets.
A function defined on sets a,b a b assigns to each element in the domain set a exactly one element from b. For example, the set 2,4,17,23 is the same as the set 17,4,23,2. Sets, relations, and functions introduction sets relations functions summary problems find, read and cite all the. Pdf fundamentals of discrete mathematical structures. Hopefully this short introduction will shed some light on what the subject is about and what you can expect as you move forward in your studies. Theres something like 7 or 8 other types of relations. 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. Discrete mathematics is the branch of mathematics dealing with objects that can consider only distinct, separated values. So far, weve seen simple structures like sets and natural numbers, but there are many other important structures out there. Basic concepts of set theory, functions and relations 1. Discrete math cheat sheetstudy sheetstudy guide in pdf. Topics 1 relations introduction relation properties equivalence relations 2 functions introduction pigeonhole principle recursion 93. Some parts are loosely adapted from the discrete computing and algorithms and software engineering modules on the bsc computer.
This course will roughly cover the following topics and speci c applications in computer science. A binary relation r from set x to y written as xry or rx, y is a subset of the cartesian product x. Relations proving symmetryantisymmetry with a defined set. Tech support more about matt392 cheat sheetstudy sheet for a discrete math class that covers sequences, recursive formulas, summation, logic, sets, power sets, functions, combinatorics, arrays and matrices. A course in discrete structures cornell university. So far, weve seen simple structures like sets and natural numbers, but there are many other important structures out.
In these discrete structures notes pdf, you will study the fundamental concepts of sets, relations and functions, mathematical logic, group theory, counting theory, probability, mathematical induction and recurrence relations, graph theory, trees and boolean algebra. Discrete mathematics functions a function assigns to each element of a set, exactly one element of a related set. Mathematical structures just as there are common data structures in programming, there are common mathematical structures in discrete math. Today, i have covered the topics functions and pigeonhole principle in the discrete structures subject and solved the corresponding net previous year. Basic building block for types of objects in discrete mathematics. Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. A binary relation r on a single set a is defined as a subset of axa. The course aims to introduce the students to boolean algebra, sets, relations, functions, principles of counting, and growth functions so. Discrete mathematics tutorial provides basic and advanced concepts of discrete mathematics. Discrete mathematics forms the mathematical foundation of computer and information science. Aslam rajmohan rajaraman eric ropiak chris burrows ravi sundaram. Functions find their application in various fields like representation of the. What are the applications of relation in discrete mathematics. Hauskrecht basic discrete structures discrete math study of the discrete structures used to represent discrete objects many discrete structures are built using sets sets collection of objects examples of discrete structures built with the help of sets.
In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Lectures 6 and 7 sets, relations, functions and counting instructor. Discrete mathematics sets relations functions free download as pdf file. R tle a x b means r is a set of ordered pairs of the form a,b where a a and b b. In this zeroone is used to represent the relationship that exists between two sets. They are an example of discrete structures and they are one of the most useful models for computer scientists and engineers in solving problems. Edaa40 discrete structures in computer science seminar 2 a. August 4 and 6, 2009 our main goal is here is to do counting using functions. This booklet consists of problem sets for a typical undergraduate discrete mathematics course aimed at computer science students. Inverse functions i every bijection from set a to set b also has aninverse function i the inverse of bijection f, written f 1, is the function that assigns to b 2 b a unique element a 2 a such that fa b. Many different systems of axioms have been proposed. Download fundamentals of discrete mathematical structures ebook free in pdf and epub format. Set operations include set union, set intersection, set difference, complement of set, and cartesian product. Discrete mathematics uses a range of techniques, some of which is seldom found in its continuous counterpart.
Direct and inverse image of a set under a relation. Cs 205 introduction to discrete structures i syllabus antonio. A oneterm introduction to discrete structures with applications to computing problems. Pdf discrete structures notes lecture free download. Discrete structures guidelines and practical list pdf discrete structures guidelines and practical list. Discrete mathematics representing relations geeksforgeeks. Discrete mathsets, relations, functions and math induction. This book covers the topics from sets, relations, functions, propositional logic, techniques of proof, lattice, algebraic structures, boolean algebra combinatorics, discrete numeric function.
Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Discrete mathset theory, relations, functions and mathematical induction. Hauskrecht basic discrete structures discrete math study of the discrete structures used to represent discrete objects many discrete structures are built using sets sets collection of objects examples of. Discrete structures guidelines and practical list pdf. Mathematics introduction and types of relations geeksforgeeks. Discrete structures lecture notes vladlen koltun1 winter 2008 1computer science department. We will use these concepts to relate different sets. Number theory athe math behind the rsa crypto system.
Applied discrete structures has been developed using pretext, a lightweight. Basic concepts of set theory, functions and relations. In this section, we introduce the set theoretic concepts of relations and functions. For two sets a and b, the operations of union, intersection, and di. The definition of a set explicitly disregards the order of the set elements, all that matters is whos in, not whos in first. Subsets a set a is a subset of a set b iff every element of a is also an element of b. Relations may exist between objects of the same set or between objects of two or more sets. Issues about data structures used to represent sets and the computational cost of set operations. What is the difference between a relation and a function from a to b. Partee 1979, fundamentals of mathematics for linguistics.
The course may not be used as part of the degree requirements for the bs degree in computer science. This chapter will be devoted to understanding set theory, relations, functions. For example, a database is viewed as a set of relations and database query languages are constructed based on operations on relations and sets. The course aims to introduce the students to boolean algebra, sets, relations, functions, principles of counting, and growth functions so that these concepts may be used effectively in other courses. Topics include sets, relations, functions, counting, graphs, trees, recursion, propositional and predicate logic, proof techniques, boolean algebra.
Discrete structures lecture notes stanford university. Discrete mathematics sets relations functions function. Sets, relations, functions introduction basic objects in. In this course you will learn the important fundamentals of discrete math set theory, relations, functions and mathematical induction with the help of 6. In this method it is easy to judge if a relation is reflexive, symmetric or transitive just by looking at the matrix. Ling 310, adapted from umass ling 409, partee lecture notes march 1, 2006 p. Our discrete mathematics structure tutorial is designed for beginners and professionals both.
Sets, functions, relations, sequences and sums colin stirling informatics colin stirling informatics discrete mathematics chaps 2. Hauskrecht relations and functions relations represent one to many relationships between elements in a and b. The union of a and b, denoted by a b, is the set that contains those elements that are either in. Sets, logic, relations, and functions andrew kay september 28, 2014 abstract this is an introductory text, not a comprehensive study. This article examines the concepts of a function and a relation a relation is any association or link between elements of one set, called the domain or less formally the set of inputs, and another set, called the range or set of outputs. Edaa40 discrete structures in computer science seminar 2 a recap.
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