Sets
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The document defines and provides examples of several concepts related to sets: - A set is an unordered collection of elements such as {1,2,3}. Repetition is irrelevant and sets are unordered. - Subsets, supersets, unions, intersections, complements and properties like commutativity and associativity are defined. - The power set of a set S is the set of all subsets of S, denoted P(S).
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The document defines basic concepts about sets including:
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For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
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SET
A set is a well defined collection of objects, called the “elements” or “members” of the set.
A specific set can be defined in two ways-
If there are only a few elements, they can be listed individually, by writing them between curly braces ‘{ }’ and placing commas in between. E.g.- {1, 2, 3, 4, 5}
The second way of writing set is to use a property that defines elements of the set.
e.g.- {x | x is odd and 0 < x < 100}
If x is an element o set A, it can be written as ‘x A’
If x is not an element of A, it can be written as ‘x A’
Special types of sets-
Standard notations used to define some sets:
N- set of all natural numbers
Z- set of all integers
Q- set of all rational numbers
R- set of all real numbers
C- set of all complex numbers
TYPES OF SETS
-subset
-singleton set
-universal set
-empty set
-finite set
-infinte set
-eual set
-disjoint set
-cardinal set
-power set
OPERATIONS ON SET
The four basic operations are:
1. Union of Sets
2. Intersection of sets
3. Complement of the Set
4. Cartesian Product of sets
Union of two given sets is the smallest set which contains all the elements of both the sets.
A B = {x | x A or x B}
Let a and b are sets, the intersection of two sets A and B, denoted by A B is the set consisting of elements which are in A as well as in B
A B = {X | x A and x B}
If A B= , the sets are said to be disjoint.
If U is a universal set containing set A, then U-A is called complement of a set.
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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,
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Only Piano ( A - B)=2
Only guitar(B-A) =3
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This document provides an overview of key concepts in set theory including:
- Elements, equal sets, subsets, power sets, union, intersection, difference, and complement operations on sets.
- Sets are defined as unordered collections of unique objects. Common set examples include integers, rationals, and reals.
- Key properties include elements, equal sets, subsets, empty sets, singleton sets, set-builder and extension notations, and Venn diagrams for representation.
- Operations on sets manipulate elements and include union, intersection, difference, and complement.
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College of Arts & Sciences
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Universal Set and Subset using Venn Diagram
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
Operations on sets
This will illustrate different operations of sets and use Venn diagrams to represent set operations.
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This document introduces set theory and its importance and applications. It defines what a set is and provides examples of different types of sets such as finite, infinite, equal, subset, power and universal sets. It describes operations on sets like union, intersection and complements. The document discusses the history of set theory and its founder Georg Cantor. It provides examples of how set theory is applied in business organization and security. Venn diagrams are introduced as a way to visualize sets. An example problem is presented to demonstrate applying set theory and Venn diagrams. The document finds that set theory is widely used in many disciplines and can be applied at different levels in business operations for problems involving intersecting and non-intersecting sets.
1. sets and basic notations
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.
Types Of Set
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.
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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.
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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.
Sets
The document discusses key concepts in set theory including:
1) Sets are collections of distinct objects that are considered as a single object. Set theory was invented by George Cantor in the late 19th century.
2) There are different ways to represent sets including roaster form using curly brackets, set builder form using properties, and Venn diagrams using circles.
3) Set operations include unions, intersections, and complements which combine sets in different ways according to their members.
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This document covers key concepts in modern algebra including equivalence relations, partial orders, functions, binary operations, permutation groups, cyclic groups, order of elements, cosets, Lagrange's theorem, normal subgroups, and quotient groups. It provides examples and definitions for each concept. Equivalence relations are defined as reflexive, symmetric, and transitive relations. Partial orders must also be antisymmetric. Functions can be one-to-one or onto. Binary operations satisfy closure and are demonstrated with examples. Permutation groups results are listed regarding even/odd permutations and inverses. Cyclic groups and the order of an element are discussed. Cosets and Lagrange's theorem relate the order of a group to the order of subgroups
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Friends if you found this helpful please click the like button. and share it :)
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This document defines basic set theory concepts including sets, elements, notation for sets, subsets, unions, intersections, and empty sets. It provides examples and notation for these concepts. Sets are collections of objects, represented with capital letters, while elements are individual objects represented with lowercase letters. Notation includes braces { } to list elements and vertical bars for set builder notation. A is a subset of B if all elements of A are also in B, written as A ⊆ B. The union of sets A and B contains all elements that are in A or B, written as A ∪ B. The intersection of sets A and B contains elements that are only in both A and B, written as A ∩ B.
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This document provides information about sets and operations on sets. It defines what a set is and gives examples of sets used in mathematics. It describes different ways to represent sets, such as roster form and set-builder form. It also defines key terms like finite and infinite sets, subsets, unions, intersections, complements and Venn diagrams. Properties of operations like union, intersection and complement are listed. In summary, the document covers fundamental concepts in set theory and operations on sets that are important foundations for mathematics.
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This document defines cyclic groups and discusses their order theorem. It explains that a cyclic group G is generated by a single element a, such that every element of G can be expressed as an power of a. It then proves that the order of a cyclic group equals the order of its generator using the division algorithm, showing that for any integer m, m can be expressed as nq + r, where n is the order of the generator and 0 <= r < n. It provides examples of applications of group theory in fields like physics, biology, crystal structure analysis, and coding theory.
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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
Dihedral groups & abeliangroups
The document discusses dihedral groups and abelian groups. It begins by defining symmetry and the different types of symmetry like line symmetry and rotational symmetry. It then discusses dihedral groups Dn which are the symmetry groups of regular n-gons, containing n rotations and n reflections. The document also discusses abelian groups, which are groups whose binary operation is commutative. It provides examples of abelian groups and properties like every subgroup of an abelian group being normal.
Introduction to Sets
SET
A set is a well defined collection of objects, called the “elements” or “members” of the set.
A specific set can be defined in two ways-
If there are only a few elements, they can be listed individually, by writing them between curly braces ‘{ }’ and placing commas in between. E.g.- {1, 2, 3, 4, 5}
The second way of writing set is to use a property that defines elements of the set.
e.g.- {x | x is odd and 0 < x < 100}
If x is an element o set A, it can be written as ‘x A’
If x is not an element of A, it can be written as ‘x A’
Special types of sets-
Standard notations used to define some sets:
N- set of all natural numbers
Z- set of all integers
Q- set of all rational numbers
R- set of all real numbers
C- set of all complex numbers
TYPES OF SETS
-subset
-singleton set
-universal set
-empty set
-finite set
-infinte set
-eual set
-disjoint set
-cardinal set
-power set
OPERATIONS ON SET
The four basic operations are:
1. Union of Sets
2. Intersection of sets
3. Complement of the Set
4. Cartesian Product of sets
Union of two given sets is the smallest set which contains all the elements of both the sets.
A B = {x | x A or x B}
Let a and b are sets, the intersection of two sets A and B, denoted by A B is the set consisting of elements which are in A as well as in B
A B = {X | x A and x B}
If A B= , the sets are said to be disjoint.
If U is a universal set containing set A, then U-A is called complement of a set.
Sets venn diagrams
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.
SETS [Algebra]
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
Sets
This document provides an overview of key concepts in set theory including:
- Elements, equal sets, subsets, power sets, union, intersection, difference, and complement operations on sets.
- Sets are defined as unordered collections of unique objects. Common set examples include integers, rationals, and reals.
- Key properties include elements, equal sets, subsets, empty sets, singleton sets, set-builder and extension notations, and Venn diagrams for representation.
- Operations on sets manipulate elements and include union, intersection, difference, and complement.
CMSC 56 | Lecture 16: Equivalence of Relations & Partial Ordering
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
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CMSC 56 | Lecture 16: Equivalence of Relations & Partial Ordering
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- A set is a collection of distinct objects called elements or members. Sets can be represented verbally or visually using lists or set-builder notation.
- Two sets are equal if they contain the same elements. Operations on sets include union, intersection, complement, difference, and Cartesian product.
- A set is finite if its elements can be counted, and infinite if its elements cannot be counted or listed with certainty. Examples demonstrate determining if a set is finite or infinite.
Sets
The document provides information about sets including definitions of key terms like union, intersection, complement, difference, properties of these operations, and counting theorems. It discusses describing sets by explicitly listing members or through a relationship. Examples are provided to illustrate concepts like subsets, proper subsets, power sets, De Morgan's laws, and using Venn diagrams to solve problems involving sets. Counting theorems are presented to calculate the number of elements in unions, intersections, and complements of finite sets.
Answers Of Discrete Mathematics
The document describes an algorithm for finding the largest integer in a list of numbers. It first defines an algorithm as a precise sequence of instructions to solve a problem. It then provides an English description of the maximum finding algorithm and expresses it in pseudocode. The algorithm assigns the first number as the maximum value, then compares each subsequent number to the current maximum, updating it if a larger number is found. It notes the algorithm uses 2n-1 comparisons to find the maximum number.
00_1 - Slide Pelengkap (dari Buku Neuro Fuzzy and Soft Computing).ppt
The document defines various concepts related to fuzzy sets and fuzzy logic. It defines the support, core, normality, crossover points, and other properties of fuzzy sets. It also defines operations on fuzzy sets like union, intersection, complement, and algebraic operations. It discusses the extension principle for mapping fuzzy sets through functions. It provides examples of applying the extension principle and compositions of fuzzy relations. Finally, it discusses linguistic variables and modifiers like hedges, negation, and connectives that are used to modify terms in a linguistic variable.
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
The document discusses key concepts about sets, including:
1) Intervals are subsets of real numbers that can be open, closed, or half-open/half-closed. Intervals are represented visually on a number line.
2) The power set of a set A contains all possible subsets of A. Its size is 2 to the power of the size of A.
3) The union of sets A and B contains all elements that are in A, B, or both. The intersection contains all elements common to both sets.
4) Practical problems can use formulas involving the sizes of unions and intersections of finite sets.
Sets
A set is an unordered collection of objects that can be defined by listing elements or describing properties that elements satisfy. Sets are used to build discrete structures like counting, combinations, relations, and graphs. A function from a set X to a set Y is a relation where each element of X is mapped to an element of Y, and no element of X is mapped to more than one element of Y. A function is one-to-one if different elements of the domain map to different elements of the codomain, and onto if every element of the codomain is mapped to by some element of the domain.
POWERPOINT (SETS & FUNCTIONS).pdf
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.
SET
This document defines and provides examples of different types of sets. It discusses the empty set, finite and infinite sets, equal sets, subsets, power sets, and the universal set. Properties of set operations like union and intersection are also covered. Visual representations of sets using Venn diagrams are described.
Set theory and Venn Diagram.docx
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
Digital text book sets
This document provides an introduction to the concept of sets in mathematics. It defines what a set is and explains that a set is a well-defined collection of distinct objects. It discusses different ways of representing sets, such as using a roster or set-builder notation. It also covers various types of sets like finite, infinite, empty, singleton, equivalent and equal sets. The document explains set operations like union, intersection and complement. It introduces Venn diagrams to visually represent relationships between sets. Finally, it discusses algebraic properties that set operations satisfy, such as commutative, associative and distributive laws.
4898850.ppt
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.
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Sets
- 1. Maths Project SETS Submitted To : Joseph Sir
- 13. Some Properties of Complement Sets 1. Complement Laws: A U A’= U A ∩ A’= 2. De Morgan’s Law: (A U B)’ = A’ ∩ B’ (A ∩ B )’ = A’ U B’ 3. Law of Double Complementation: ( A’ )’ = A 4. Laws of Empty Set and Universal Set: ’ = U U’ =
- 14. THANK YOU Done By : Sukesh XI- B