About sets , definition example, and some types of set. Explained the some operation of set like union of set and intersection of set with usual number example
The document defines and provides examples of different types of sets:
1. Empty/null sets contain no elements. Singleton sets contain only one element. Finite sets contain a finite number of elements, while infinite sets are not finite.
2. Subsets contain elements of another set. Proper subsets are subsets that are not equal to the original set. Power sets are the set of all subsets of a given set.
3. Examples are given of empty, singleton, finite, infinite, equivalent, equal, subset, and proper subset sets. Cardinal numbers represent the number of elements in a set.
A set is a collection of distinct objects called elements or members. A set can be defined using a roster method that lists the elements within curly brackets, or a rule method that describes a characteristic property that determines the elements. The cardinality of a set refers to the number of elements it contains, and can be finite or infinite.
This document provides an introduction to set theory. It defines what a set is and provides examples of common sets. A set can be represented in roster form by listing its elements within curly brackets or in set builder form using a characteristic property. There are different types of sets such as finite sets, infinite sets, empty sets, singleton sets, and power sets which contain all subsets. Set operations like union, intersection, difference and symmetric difference are introduced. Important concepts like subsets, equivalent sets, disjoint sets and complements are also covered.
Introduction to Sets and Set Operations. The presentation include contents of a KWLH Chart, Essential Questions, and Self-Assessment Questions. With exploration and formative assessments.
The document defines set concepts and their properties. It explains that a set is a collection of distinct objects, called elements. Properties discussed include how sets are denoted, elements belong or don't belong to sets, order doesn't matter, and counting each element once. It also covers set theory, Venn diagrams, ways to represent sets, types of sets (empty, finite, infinite), equal sets, subsets, cardinality, and operations like intersection, union, difference, and complement of sets. Examples are provided to illustrate each concept.
Sections Included:
1. Collection
2. Types of Collection
3. Sets
4. Commonly used Sets in Maths
5. Notation
6. Different Types of Sets
7. Venn Diagram
8. Operation on sets
9. Properties of Union of Sets
10. Properties of Intersection of Sets
11. Difference in Sets
12. Complement of Sets
13. Properties of Complement Sets
14. De Morgan’s Law
15. Inclusion Exclusion Principle
A set is a collection of distinct objects. There are two ways to describe a set: roster form lists the elements between braces, and set-builder form uses a characteristic property P(x). Sets can be infinite, finite, empty, or singleton. Two sets are equal if they contain the same elements, and equivalent if they have the same number of elements. A set is a subset if all its elements are contained in another set, called the superset. Closed and open intervals are examples of subsets of real numbers. The power set is the collection of all subsets, and the universal set contains all sets in a given context. Venn diagrams use circles and rectangles to represent relationships between sets. Common set operations include union
The document defines and provides examples of different types of sets:
1. Empty/null sets contain no elements. Singleton sets contain only one element. Finite sets contain a finite number of elements, while infinite sets are not finite.
2. Subsets contain elements of another set. Proper subsets are subsets that are not equal to the original set. Power sets are the set of all subsets of a given set.
3. Examples are given of empty, singleton, finite, infinite, equivalent, equal, subset, and proper subset sets. Cardinal numbers represent the number of elements in a set.
A set is a collection of distinct objects called elements or members. A set can be defined using a roster method that lists the elements within curly brackets, or a rule method that describes a characteristic property that determines the elements. The cardinality of a set refers to the number of elements it contains, and can be finite or infinite.
This document provides an introduction to set theory. It defines what a set is and provides examples of common sets. A set can be represented in roster form by listing its elements within curly brackets or in set builder form using a characteristic property. There are different types of sets such as finite sets, infinite sets, empty sets, singleton sets, and power sets which contain all subsets. Set operations like union, intersection, difference and symmetric difference are introduced. Important concepts like subsets, equivalent sets, disjoint sets and complements are also covered.
Introduction to Sets and Set Operations. The presentation include contents of a KWLH Chart, Essential Questions, and Self-Assessment Questions. With exploration and formative assessments.
The document defines set concepts and their properties. It explains that a set is a collection of distinct objects, called elements. Properties discussed include how sets are denoted, elements belong or don't belong to sets, order doesn't matter, and counting each element once. It also covers set theory, Venn diagrams, ways to represent sets, types of sets (empty, finite, infinite), equal sets, subsets, cardinality, and operations like intersection, union, difference, and complement of sets. Examples are provided to illustrate each concept.
Sections Included:
1. Collection
2. Types of Collection
3. Sets
4. Commonly used Sets in Maths
5. Notation
6. Different Types of Sets
7. Venn Diagram
8. Operation on sets
9. Properties of Union of Sets
10. Properties of Intersection of Sets
11. Difference in Sets
12. Complement of Sets
13. Properties of Complement Sets
14. De Morgan’s Law
15. Inclusion Exclusion Principle
A set is a collection of distinct objects. There are two ways to describe a set: roster form lists the elements between braces, and set-builder form uses a characteristic property P(x). Sets can be infinite, finite, empty, or singleton. Two sets are equal if they contain the same elements, and equivalent if they have the same number of elements. A set is a subset if all its elements are contained in another set, called the superset. Closed and open intervals are examples of subsets of real numbers. The power set is the collection of all subsets, and the universal set contains all sets in a given context. Venn diagrams use circles and rectangles to represent relationships between sets. Common set operations include union
A function is a relation between a set of inputs (domain) and set of outputs (codomain) where each input is mapped to exactly one output. There are different types of functions such as one-to-one, onto, bijective, many-to-one, and inverse functions. Functions can be represented graphically or using function notation such as f(x). Common functions include polynomial, trigonometric, exponential, logarithmic, and composite functions which are the composition of two simpler functions.
Venn diagrams are used to represent relationships between sets. They can show disjoint sets with no common elements, overlapping sets that share some elements, unions that combine elements, intersections that show only shared elements, complements that show elements not in the given set, and subsets where all elements of one set are contained within another set. Key elements of Venn diagrams include circles to represent sets, shading to indicate elements in operations like unions and intersections, and a universal set that contains all elements being considered.
This document defines functions and related terminology such as domain, codomain, range, one-to-one functions, onto functions, and bijections. It provides examples of graphical representations of functions and discusses concepts like whether a function is one-to-one or onto based on its graph. The pigeonhole principle is also introduced as stating that if more items are put into fewer containers, at least one container must hold multiple items.
CMSC 56 | Lecture 16: Equivalence of Relations & Partial Orderingallyn joy calcaben
Equivalence of Relations & Partial Ordering
CMSC 56 | Discrete Mathematical Structure for Computer Science
November 21, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
This document introduces some basic concepts in set theory. It defines a set as a structure representing an unordered collection of distinct objects. Set theory deals with operations on sets such as union, intersection, difference and relations between sets. It provides notations for sets and examples of basic properties of sets like equality, subsets, empty sets and infinite sets. The document also introduces concepts like cardinality, power sets, Cartesian products and Venn diagrams to represent relationships between sets.
This document provides an overview of set theory concepts including:
1. It defines what a set is and introduces some key terms like members, elements, and operations between sets.
2. It outlines several ways to represent sets including using rosters/lists and describing characteristic properties.
3. It discusses set notation where sets are denoted by capital letters and explains membership.
4. It describes different types of sets such as finite, infinite, null, singleton, and disjoint sets.
This document defines and describes several key concepts in set theory:
1. A set is a collection of well-defined objects that can be clearly distinguished from one another. Examples of sets include the set of natural numbers from 1 to 50.
2. Sets can be described using either the roster method, which lists the elements within curly brackets, or the set-builder method, which defines a property for the elements.
3. Types of sets include the empty set, singleton sets containing one element, finite sets that can be counted, infinite sets that cannot be counted, equivalent sets with the same number of elements, and subsets where all elements of one set are contained within another set.
This document provides an overview of basic set theory concepts including defining and representing sets, the number of elements in a set, comparing sets, subsets, and operations on sets including union and intersection. Key points covered are defining a set as a collection of well-defined objects, representing sets using listing, defining properties, or Venn diagrams, defining the cardinal number of a set as the number of elements it contains, comparing sets as equal or equivalent based on elements, defining subsets as sets contained within other sets, and defining union as the set of elements in either set and intersection as the set of elements common to both sets.
This document discusses set operations and identities. It defines operations like union, intersection, complement, difference, and cardinality. It presents examples of calculating unions, intersections, complements, and differences of sets. It also covers set identities like commutative, associative, distributive, De Morgan's laws, and absorption laws. Methods for proving identities like subset proofs and membership tables are described. An example proof of the second De Morgan's law is provided using subset notation.
The document explains Venn diagrams and set operations. It introduces the universal set of ten best friends and defines subsets for friends who play soccer, tennis, or volleyball. It then demonstrates set operations like union, intersection, difference and complement using these friend sets in Venn diagrams and symbolic notation. Key concepts covered are the universal set, set elements, unions, intersections, differences, and the empty set.
The document discusses sets, relations, and functions. It begins by providing examples of well-defined and not well-defined collections to introduce the concept of a set. A set is defined as a collection of well-defined objects. Standard notations for sets are introduced. Sets can be represented using a roster method by listing elements or a set-builder form using a common property. Sets are classified as finite or infinite based on the number of elements, and other set types like the empty set and singleton set are defined. Equal, equivalent, and disjoint sets are also defined.
The document discusses set operations and Venn diagrams. It defines the basic set operations of intersection, union, and complement. Intersection refers to elements common to two sets, union refers to all elements in either set, and complement refers to elements not in the set. Venn diagrams use circles or regions to visually represent sets and the relationships between them. Examples demonstrate using Venn diagrams to illustrate different set operations like intersection, union, and complement. Exercises involve identifying the appropriate Venn diagram shading for expressions involving these operations.
Know the basics on sets such as the methods of writing sets, the cardinality of a set, null and universal sets, equal and equivalents sets, and many more.
Identifying universal, equal and equivalent sets,MartinGeraldine
This document defines and provides examples of universal sets, equal sets, equivalent sets, joint sets, and disjoint sets.
A universal set U contains all elements under consideration, including the sets themselves. Two sets A and B are equal if they contain the same elements. Sets C and D are equivalent if they have the same number of elements, even if the elements themselves are different. Joint sets have common elements, while disjoint sets have no common elements. Examples are provided to illustrate each concept.
This document defines and explains various concepts related to sets and relations. It discusses the four main set operations of union, intersection, complement, and difference. It then explains eight types of relations: empty, universal, identity, inverse, reflexive, symmetric, transitive, and equivalence relations. Finally, it defines partial ordering as a relation that is reflexive, antisymmetric, and transitive.
Set theory is a branch of mathematics that studies sets and their properties. A set is a collection of distinct objects, which can include numbers, points, or other sets. Some key concepts in set theory include:
- Membership and subsets, where an object is a member of a set and a set is a subset of another if all its members are also in the other set.
- Binary operations on sets like union, intersection, and complement/difference.
- The power set, which contains all possible subsets of a given set.
- Finite and infinite sets, with finite sets having a definite number of members and infinite sets not having an end. The empty set contains no members.
The document defines basic concepts about sets including:
- A set is a collection of distinct objects called elements. Sets can be represented using curly brackets or the set builder method.
- Common set symbols are defined such as belongs to (∈), is a subset of (⊆), and is not a subset of (⊄).
- Types of sets like empty sets, singleton sets, finite sets, and infinite sets are described.
- Operations between sets such as union, intersection, difference, and complement are explained using Venn diagrams.
- Laws for sets like commutative, associative, distributive, double complement, and De Morgan's laws are listed.
- An example problem calculates
The answer for:
1)Give me a group of girls whose height is > than 156 cm is E,F,G.
2) The answers for Piano and Guitar question is:
n(U) =8,
n(A)=3,
n(B)=4
(A n B) = 1
( A U B)= 6
(A U B)' = 2
Only Piano ( A - B)=2
Only guitar(B-A) =3
Sets [Algebra] in an easier and interesting way to learn! Specially suited for young children and for those who find Sets difficult to grasp.
Content-
Venn diagram,
Set builder(Rule method),
List method(Roster method),
Universal set,
Union of sets,
Intersection of set
This document discusses sets, functions, and relations. It begins by defining key terms related to sets such as elements, subsets, operations on sets using union, intersection, difference and complement. It then discusses relations and functions, defining a relation as a set of ordered pairs where the elements are related based on a given condition. Functions are introduced as a special type of relation where each element of the domain has a single element in the range. The document aims to help students understand and use the properties and notations of sets, functions, and relations, and appreciate their importance in real-life situations.
A function is a relation between a set of inputs (domain) and set of outputs (codomain) where each input is mapped to exactly one output. There are different types of functions such as one-to-one, onto, bijective, many-to-one, and inverse functions. Functions can be represented graphically or using function notation such as f(x). Common functions include polynomial, trigonometric, exponential, logarithmic, and composite functions which are the composition of two simpler functions.
Venn diagrams are used to represent relationships between sets. They can show disjoint sets with no common elements, overlapping sets that share some elements, unions that combine elements, intersections that show only shared elements, complements that show elements not in the given set, and subsets where all elements of one set are contained within another set. Key elements of Venn diagrams include circles to represent sets, shading to indicate elements in operations like unions and intersections, and a universal set that contains all elements being considered.
This document defines functions and related terminology such as domain, codomain, range, one-to-one functions, onto functions, and bijections. It provides examples of graphical representations of functions and discusses concepts like whether a function is one-to-one or onto based on its graph. The pigeonhole principle is also introduced as stating that if more items are put into fewer containers, at least one container must hold multiple items.
CMSC 56 | Lecture 16: Equivalence of Relations & Partial Orderingallyn joy calcaben
Equivalence of Relations & Partial Ordering
CMSC 56 | Discrete Mathematical Structure for Computer Science
November 21, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
This document introduces some basic concepts in set theory. It defines a set as a structure representing an unordered collection of distinct objects. Set theory deals with operations on sets such as union, intersection, difference and relations between sets. It provides notations for sets and examples of basic properties of sets like equality, subsets, empty sets and infinite sets. The document also introduces concepts like cardinality, power sets, Cartesian products and Venn diagrams to represent relationships between sets.
This document provides an overview of set theory concepts including:
1. It defines what a set is and introduces some key terms like members, elements, and operations between sets.
2. It outlines several ways to represent sets including using rosters/lists and describing characteristic properties.
3. It discusses set notation where sets are denoted by capital letters and explains membership.
4. It describes different types of sets such as finite, infinite, null, singleton, and disjoint sets.
This document defines and describes several key concepts in set theory:
1. A set is a collection of well-defined objects that can be clearly distinguished from one another. Examples of sets include the set of natural numbers from 1 to 50.
2. Sets can be described using either the roster method, which lists the elements within curly brackets, or the set-builder method, which defines a property for the elements.
3. Types of sets include the empty set, singleton sets containing one element, finite sets that can be counted, infinite sets that cannot be counted, equivalent sets with the same number of elements, and subsets where all elements of one set are contained within another set.
This document provides an overview of basic set theory concepts including defining and representing sets, the number of elements in a set, comparing sets, subsets, and operations on sets including union and intersection. Key points covered are defining a set as a collection of well-defined objects, representing sets using listing, defining properties, or Venn diagrams, defining the cardinal number of a set as the number of elements it contains, comparing sets as equal or equivalent based on elements, defining subsets as sets contained within other sets, and defining union as the set of elements in either set and intersection as the set of elements common to both sets.
This document discusses set operations and identities. It defines operations like union, intersection, complement, difference, and cardinality. It presents examples of calculating unions, intersections, complements, and differences of sets. It also covers set identities like commutative, associative, distributive, De Morgan's laws, and absorption laws. Methods for proving identities like subset proofs and membership tables are described. An example proof of the second De Morgan's law is provided using subset notation.
The document explains Venn diagrams and set operations. It introduces the universal set of ten best friends and defines subsets for friends who play soccer, tennis, or volleyball. It then demonstrates set operations like union, intersection, difference and complement using these friend sets in Venn diagrams and symbolic notation. Key concepts covered are the universal set, set elements, unions, intersections, differences, and the empty set.
The document discusses sets, relations, and functions. It begins by providing examples of well-defined and not well-defined collections to introduce the concept of a set. A set is defined as a collection of well-defined objects. Standard notations for sets are introduced. Sets can be represented using a roster method by listing elements or a set-builder form using a common property. Sets are classified as finite or infinite based on the number of elements, and other set types like the empty set and singleton set are defined. Equal, equivalent, and disjoint sets are also defined.
The document discusses set operations and Venn diagrams. It defines the basic set operations of intersection, union, and complement. Intersection refers to elements common to two sets, union refers to all elements in either set, and complement refers to elements not in the set. Venn diagrams use circles or regions to visually represent sets and the relationships between them. Examples demonstrate using Venn diagrams to illustrate different set operations like intersection, union, and complement. Exercises involve identifying the appropriate Venn diagram shading for expressions involving these operations.
Know the basics on sets such as the methods of writing sets, the cardinality of a set, null and universal sets, equal and equivalents sets, and many more.
Identifying universal, equal and equivalent sets,MartinGeraldine
This document defines and provides examples of universal sets, equal sets, equivalent sets, joint sets, and disjoint sets.
A universal set U contains all elements under consideration, including the sets themselves. Two sets A and B are equal if they contain the same elements. Sets C and D are equivalent if they have the same number of elements, even if the elements themselves are different. Joint sets have common elements, while disjoint sets have no common elements. Examples are provided to illustrate each concept.
This document defines and explains various concepts related to sets and relations. It discusses the four main set operations of union, intersection, complement, and difference. It then explains eight types of relations: empty, universal, identity, inverse, reflexive, symmetric, transitive, and equivalence relations. Finally, it defines partial ordering as a relation that is reflexive, antisymmetric, and transitive.
Set theory is a branch of mathematics that studies sets and their properties. A set is a collection of distinct objects, which can include numbers, points, or other sets. Some key concepts in set theory include:
- Membership and subsets, where an object is a member of a set and a set is a subset of another if all its members are also in the other set.
- Binary operations on sets like union, intersection, and complement/difference.
- The power set, which contains all possible subsets of a given set.
- Finite and infinite sets, with finite sets having a definite number of members and infinite sets not having an end. The empty set contains no members.
The document defines basic concepts about sets including:
- A set is a collection of distinct objects called elements. Sets can be represented using curly brackets or the set builder method.
- Common set symbols are defined such as belongs to (∈), is a subset of (⊆), and is not a subset of (⊄).
- Types of sets like empty sets, singleton sets, finite sets, and infinite sets are described.
- Operations between sets such as union, intersection, difference, and complement are explained using Venn diagrams.
- Laws for sets like commutative, associative, distributive, double complement, and De Morgan's laws are listed.
- An example problem calculates
The answer for:
1)Give me a group of girls whose height is > than 156 cm is E,F,G.
2) The answers for Piano and Guitar question is:
n(U) =8,
n(A)=3,
n(B)=4
(A n B) = 1
( A U B)= 6
(A U B)' = 2
Only Piano ( A - B)=2
Only guitar(B-A) =3
Sets [Algebra] in an easier and interesting way to learn! Specially suited for young children and for those who find Sets difficult to grasp.
Content-
Venn diagram,
Set builder(Rule method),
List method(Roster method),
Universal set,
Union of sets,
Intersection of set
This document discusses sets, functions, and relations. It begins by defining key terms related to sets such as elements, subsets, operations on sets using union, intersection, difference and complement. It then discusses relations and functions, defining a relation as a set of ordered pairs where the elements are related based on a given condition. Functions are introduced as a special type of relation where each element of the domain has a single element in the range. The document aims to help students understand and use the properties and notations of sets, functions, and relations, and appreciate their importance in real-life situations.
This document provides an overview of basic discrete mathematical structures including sets, functions, sequences, sums, and matrices. It begins by defining a set as an unordered collection of elements and describes various ways to represent sets, such as listing elements or using set-builder notation. It then discusses operations on sets like unions, intersections, complements, and Cartesian products. Finally, it introduces functions as assignments of elements from one set to another. The document serves as an introduction to fundamental discrete structures used throughout mathematics.
A power point presentation on the topic SETS of class XI Mathematics. it includes all the brief knowledge on sets like their intoduction, defination, types of sets with very intersting graphics n presentation.
The document defines basic set theory concepts including:
- A set is a collection of distinct objects called elements.
- Sets can be represented using curly brackets or set builder notation.
- The empty set, subsets, proper subsets, unions, intersections and complements are defined.
- Cardinality refers to the number of elements in a finite set.
- Power sets are the set of all subsets of a given set.
This document defines and describes various types of sets and set operations. It defines sets such as the set of natural numbers N, integers Z, rational numbers Q, and real numbers R. It describes how sets can be defined using roster form or set-builder form. It also defines finite and infinite sets, empty sets, subsets, power sets, unions, intersections, complements, Cartesian products, Venn diagrams, and De Morgan's laws for set operations.
After going through this module, you are expected to:
• define well-defined sets and other terms associated to sets
• write a set in two different forms;
• determine the cardinality of a set;
• enumerate the different subsets of a set;
• distinguish finite from infinite sets; equal sets from equivalent sets
• determine the union, intersection of sets and the difference of two sets
The document provides information about sets, relations, and functions in mathematics:
- A set is a collection of distinct objects, called elements or members. Sets are represented using curly brackets and elements are separated by commas. There are finite and infinite sets. Operations on sets include union, intersection, complement, difference, and power set.
- A relation from a set A to a set B is a subset of the Cartesian product A × B. The domain is the set of first elements in the relation and the range is the set of second elements.
- A function from a set A to a set B is a special type of relation where each element of A is mapped to exactly one element of B.
Set and Set operations, UITM KPPIM DUNGUNbaberexha
This document defines sets and common set operations such as union, intersection, difference, complement, Cartesian product, and cardinality. It begins by defining a set as a collection of distinct objects and provides examples of sets. It then discusses ways to represent and visualize sets using listings, set-builder notation, Venn diagrams, and properties of subsets, supersets, equal sets, disjoint sets, and infinite sets. The document concludes by defining common set operations and identities using membership tables and examples.
This document discusses four basic concepts in mathematics: sets and operations on sets, relations, functions, and binary operations. It provides definitions and examples of key terms related to sets, including elements of a set, subsets, union, intersection, difference, complement, and Cartesian product. Operations on sets such as union, intersection, and difference are defined using set notation. Examples are given to illustrate concepts like subsets, equal sets, disjoint sets, and the Cartesian product.
This document defines and explains key concepts in sets and set theory, including:
- Defining sets and listing elements using roster and set-builder notation
- Important mathematical sets like natural numbers, integers, and real numbers
- Describing relationships between sets such as subsets, equality, and Venn diagrams
- Calculating cardinality to determine the number of elements in a set
- Forming Cartesian products to combine elements from multiple sets into ordered pairs
1. The document discusses 8 key points about set theory including the empty set, singleton sets, finite and infinite sets, union and intersection of sets, difference of sets, subsets, and disjoint sets.
2. The empty set, denoted by Φ, contains no elements and has 0 elements. A singleton set contains only one element. A set is finite if it contains a finite number of elements and infinite if it contains an infinite number of elements.
3. The union of sets involves all elements that belong to any of the sets. The intersection of sets is the set of all elements common to all sets. The difference of sets involves elements in one set that are not in another. Two sets are disjoint if
The document provides information about sets including:
1) Sets can be finite, infinite, empty, or singleton and are represented using curly brackets. Common set operations are union, intersection, and complement.
2) A set's cardinality refers to the number of elements it contains. Subsets are sets contained within other sets.
3) Examples are given of representing sets using roster and set-builder methods and performing set operations like union, intersection, and complement on sample sets.
4) Basic properties of sets like idempotent, commutative, and associative laws for simplifying set expressions are outlined.
The document defines sets and provides examples of different types of sets. It discusses how sets can be defined using roster notation by listing elements within braces or using set-builder notation stating properties elements must have. Some key types of sets mentioned include the empty set, natural numbers, integers, rational numbers, and real numbers. Operations on sets like union, intersection, and difference are introduced along with examples. Subsets, Venn diagrams, and the power set are also covered.
The document defines key concepts in set theory including:
1. A set is a well-defined collection of distinct objects called elements. Georg Cantor is credited with creating set theory.
2. Sets can be represented in roster form by listing elements within curly brackets or in set-builder form using properties the elements share.
3. Operations on sets include intersection, union, difference, and complement. Intersection is the set of common elements, union is all elements in either set, difference is elements only in the first set, and complement is elements not in the set.
This document defines fundamental concepts in set theory, including:
- Sets are collections of distinct objects called elements or members. Capital letters denote sets and lowercase letters denote elements.
- There are two main ways to specify a set - by listing its elements or describing their common properties.
- Set relationships include subset (all elements of one set are in another), equality (sets have the same elements), and disjoint (sets have no elements in common).
- Set operations include union (elements in either set), intersection (elements in both sets), complement (elements not in the set), difference (elements in the first set not in the second), and symmetric difference (elements in either set but not both).
- Venn
This document provides an overview of set theory, including definitions and concepts. It begins by defining a set as a collection of distinct objects, called elements or members. It describes how sets are denoted and provides examples. Key concepts covered include subsets, the empty set, set operations like union and intersection, and properties of sets. The document also discusses topics like the power set, Cartesian products, partitions, and the universal set. Overall, it serves as a comprehensive introduction to the basic ideas and terminology of set theory.
1. A set is a collection of distinct objects or elements that have some common property. Sets are represented using curly braces and capital letters. Elements within a set should not be repeated.
2. There are two main methods to define a set - the roster method which lists all elements, and the set builder method which describes the property defining membership.
3. There are several types of sets including finite sets with a set number of elements, infinite sets, singleton sets with one element, empty sets with no elements, equal sets with the same elements, and subsets which are sets within other sets.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
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What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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3. SETS
A set is a well-defined collection of objects.
Here well- defined means it must be particular with reference to all
The following points may be noted in writing sets:
(i) Objects, elements and members of a set are synonymous terms.
(ii) Sets are usually denoted by capital letters A, B, C, X, Y, Z, etc.
(iii) The elements of a set are represented by small letters a, b, c, x, y,
For example :
A={ s,a,k,l,e,h,p,u,r}
Here A is set and s,a,k,l,e,p,u,r are element
4. REPRESENTATION OF SET
There are two methods of representing a set :
(i) Roster or tabular form
(ii) Set-builder form.
Roster or tabular form
In roster form, all the elements of a set are listed, the elements are being
separated by commas and are enclosed within braces
● in roaster form, the elements are distinct
Example
Multiple of 3 between 1 and31 is {3,6,9,12,15,18,21,24,27,30}
The word ‘college’ written in roaster form as {c,o,l,e,g}
5. Set-builder form
All the elements of a set possess a single common property
Which is not possessed by any element outside the set.
Example:
V={x : x=vowels in English alphabet}
R={ y: y=colors in rainbow}
Roster form Set builder form
O={1,3,5,7,9} O={x : x=odd number below 10}
6. Empty set: A set which does not contain any element is called the empty
set or the void set or null set and is denoted by { } or φ.
Finite and infinite set: A set which consists of a finite number of
elements is called a finite set otherwise, the set is called an infinite set.
Example
Finite set => A={1,2,3,4,5,6,7,8,9}
Infinite set=> S={Number of stars in sky}
Subset: A set A is said to be a subset of set B if every element of A is also
an element of B.
In symbols, A ⊂ B if a ∈ A ⇒ a ∈ B.
Example A={1,2,3,4,5,6} and B={2,3,6,}
A ⊂ B
7. Equal set: Given two sets A and B, if every elements of A is also an
element of B and if every element of B is also an element of A, then
the sets A and B are said to be equal.
If A={2,4,6,8} and B={2,4,6,8}
Then set Aand set B are equal set
Intervals as subsets of R
Let a, b ∈ R and a < b. Then
(a) An open interval denoted by (a, b) is the set of real numbers {x : a
< x < b} this imples all elements between a & b expect a, b
(b) A closed interval denoted by [a, b] is the set of real numbers {x : a
≤ x ≤ b) Means all elements between a &b and a,b
(c) Intervals closed at one end and open at the other are given by
[a, b) = {x : a ≤ x < b} (a, b] = {x : a < x ≤ b}
8. Power set: The collection of all subsets of a set A is called the power set of A.
• it is denoted by P(A).
• If the number of elements in A = n , i.e., n(A) = n, then thenumber of
elements in P(A) = 2n
Universal set :
• This is a basic set.
• in a particular context whose elements and subsets are relevant to that
particular context.
• It is denoted by English aphabet letter U
Example ,
for the set of vowels in the English alphabet, the universal set can be the
set of all alphabets in English. Universal
10. Union of Sets : The union of any two given sets A and B is the set C which
consists of all those elements which are either in A or in B.
In symbols, we write C = A ∪ B = {x | x ∈A or x ∈B}
Example
1. A={ 1,2,3,4} B={5,6,7,8}
C= A ∪ B = {1,2,3,4,5,6 7,8}
2. D={2,3,6,7} E={1,3,7,8,9}
F = D ∪ E = {2,3,6,7,1,8,9} or {1,2,3,6,7,8,9}
Some properties of the operation of union.
(i) A ∪ B = B ∪ A
(ii) (A ∪ B) ∪ C = A ∪ (B ∪ C)
(iii) A ∪ φ = A (iv) A ∪ A = A
(v) U ∪ A = U
11. Intersection of sets:
The intersection of two sets A and B is the set which consists of all those
elements which belong to both A and B.
■ Intersection of set is denoted by ‘∩’
■ Symbolically, A ∩ B = {x : x ∈ A and x ∈ B}
■ When A ∩ B = φ, then A and B are called disjoint sets.
Example
1. A={1,4,5,9} B={1,9,4,7}
A ∩ B ={1,4,9}
2. C={2,4,7} D={1,3,5}
C ∩ D = φ
Some properties of the operation of intersection
(i) A ∩ B = B ∩ A (ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)
(iii) φ ∩ A = φ ; U ∩ A = A (iv) A ∩ A = A
(v) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
(vi) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)