This presentation describes Matrices and Determinants in detail including all the relevant definitions with examples, various concepts and the practice problems.
This presentation describes Matrices and Determinants in detail including all the relevant definitions with examples, various concepts and the practice problems.
This PPT will clarify your all doubts in Arithmetic Progression.
Please download this PPT and if any doubt according to this PPT, please comment , then i will try to solve your problem.
Thank you :)
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.
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10mayank78610
THIS A PROJECT BEING MADE BY INFORMATION COLLECTED FROM CLASS 10 MATHS NCERT BOOK.
THANK YOU FOR SEEING MY PROJECT ... I THINK THIS MIGHT HELP YOU IN YOUR HOLIDAY HOMEWORK PROJECTS .
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.
This PPT will clarify your all doubts in Arithmetic Progression.
Please download this PPT and if any doubt according to this PPT, please comment , then i will try to solve your problem.
Thank you :)
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.
PROJECT (PPT) ON PAIR OF LINEAR EQUATIONS IN TWO VARIABLES - CLASS 10mayank78610
THIS A PROJECT BEING MADE BY INFORMATION COLLECTED FROM CLASS 10 MATHS NCERT BOOK.
THANK YOU FOR SEEING MY PROJECT ... I THINK THIS MIGHT HELP YOU IN YOUR HOLIDAY HOMEWORK PROJECTS .
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.
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
This slide help in the study of those students who are enrolled in BSCS BSC computer MSCS. In this slide introduction about discrete structure are explained. As soon as I upload my next lecture on proposition logic.
In mathematics, a set is defined as a collection of distinct, well-defined objects forming a group. There can be any number of items, be it a collection of whole numbers, months of a year, types of birds, and so on. Each item in the set is known as an element of the set. We use curly brackets while writing a set.
Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
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Power Point Presentation on GREEN CHEMISTRY
(info on pollution, causes and its prevention)
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This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
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The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
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This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Home assignment II on Spectroscopy 2024 Answers.pdf
Mathematics class XI SETS
1.
2. The theory of sets was
developed by German
mathematician Georg Cantor
(1845-1918). He first
encountered sets while working
on “Problems on Trigonometric
Series” . SETS are being used in
mathematics problem since they
were discovered.
3. Collection of object of a particular kind,
such as, a pack of cards, a crowed of
people, a cricket team etc. In mathematics
of natural number, prime numbers etc.
4. A set is a well defined collection of
objects.
Elements of a set are synonymous
terms.
Sets are usually denoted by capital
letters.
Elements of a set are represented by
small letters.
5. There are two ways to represent sets
Roster or tabular form.
Set-builder form.
6. ROSTER OR TABULAR
FORM
In roster form, all the elements of set are
listed, the elements are being separated
by commas and are enclosed within
braces { }.
e.g. :
set of 1,2,3,4,5,6,7,8,9,10.
{1,2,3,4,5,6,7,8,9,10}
7. SET-BUILDER FORM
In set-builder form, all the elements of a
set possess a single common property
which is not possessed by an element
outside the set.
e.g. : set of natural numbers k
k= {x : x is a natural number}
8. EXAMPLE OF SETS IN
MATHS
N : the set of all natural numbers
Z : the set of all integers
Q : the set of all rational numbers
R : the set of all real numbers
Z+ : the set of positive integers
Q+ : the set of positive rational numbers
R+ : the set of positive real numbers.
10. THE EMPTY SET
A set which doesn't contains any element is
called the empty set or null set or void set,
denoted by symbol ϕ or { }.
e.g. : let R = {x : 1< x < 2, x is a natural
number}
11. FINITE & INFINITE SETS
A set which is empty or consist of a definite
numbers of elements is called finite
otherwise, the set is called infinite.
e.g. : let k be the set of the days of the week.
Then k is finite
let R be the set of points on a line.
Then R is infinite
12. EQUAL SETS
Given two sets K & r are said to be equal
if they have exactly the same element and
we write K=R. otherwise the sets are said
to be unequal and we write K=R.
e.g. : let K = {1,2,3,4} & R= {1,2,3,4}
then K=R
13. SUBSETS
A set R is said to be subset of a set K if
every element of R is also an element K.
R⊂K
This mean all the elements of R contained
in K
14. POWER SET
The set of all subset of a given set
is called power set of that set.
The collection of all subsets of a set
K is called the power set of
denoted by P(K).In P(K) every
element is a set.
If K= [1,2}
P(K) = {ϕ, {1}, {2}, {1,2}}
15. UNIVERSAL SET
Universal set is set which contains all
object, including itself.
e.g. : the set of real number would be the
universal set of all other sets of number.
NOTE : excluding negative root
16. SUBSETS OF R
The set of natural numbers N= {1,2,3,4,....}
The set of integers Z= {…,-2, -1, 0, 1, 2,
3,…..}
The set of rational numbers Q= {x : x =
p/q, p, q ∈ Z and q ≠ 0
NOTE : members of Q also include negative
numbers.
17. INTERVALS OF SUBSETS
OF R
OPEN INTERVAL
The interval denoted as (a, b), a &b are
real numbers ; is an open interval, means
including all the element between a to b
but excluding a &b.
18. CLOSED INTERVAL
The interval denoted as [a, b], a &b are
Real numbers ; is an open interval,
means including all the element between
a to b but including a &b.
19. TYPES OF INTERVALS
(a, b) = {x : a < x < b}
[a, b] = {x : a ≤ x ≤ b}
[a, b) = {x : a ≤ x < b}
(a, b) = {x : a < x ≤ b}
20. HISTORY OF VENN
DIAGRAM
A Venn diagram or set diagram is a diagram
that shows all possible logical relations between
a finite collection of sets. Venn diagrams were
conceived around 1880 by John Venn. They are
used to teach elementary set theory, as well as
illustrate simple set relationships
in probability, logic, statistics linguistics and co
mputer science.
21. Venn consist of rectangles and closed
curves usually circles. The universal is
represented usually by rectangles and its
subsets by circle.
22. ILUSTRATION 1. in fig U= { 1, 2 , 3, …..,
10 } is the universal set of which A = { 2, 4, 3,
……, 10} is a subset.
.2
.1
.5
.9
.8
.3
.4
.6
.10
.7
23. ILLUSTRATION 2. In fig U = { 1, 2, 3, ….,
10 } is the universal set of which A = { 2, 4, 6,
8, 10 } and B = { 4, 6 } are subsets, and also B
⊂A
.2
.1
A
.3
B
.8
.9
.4
.6
. 10
.5
.7
24. OPERATIONS ON SETS
UNION OF SETS : the union of two sets A and B
is the set C which consist of all those element which
are either in A or B or in both.
PURPLE part is
the union
AUB
(UNION)
25. SOME PROPERTIES OF THE
OPERATION OF UNION
1) A U B = B U A
( commutative law )
2) ( A U B ) U C = A U ( B U C )
( associative law )
3) A U ϕ = A
( law of identity element )
4) A U A = A
( idempotent law )
5) U U A = A ( law of U )
26. SOME PROPERTIES OF THE
OPERATION OF INTERSECTION
1) A ∩ B = B ∩ A
( commutative law )
2) ( A ∩ B ) ∩ C = A ∩ ( B ∩ C )
( associative law )
3) Φ ∩ A = Φ, U ∩ A = A
( law of Φ and
U)
4) A ∩ A = A
( idempotent law )
5) A ∩ ( B U C ) = ( A ∩ B ) U ( A ∩ C )
( distributive law )
27. COMPLEMENT OF SETS
Let U = { 1, 2, 3, } now the set of all those
element of U which doesn‟t belongs to A will
be called as A compliment.
A’
U
A
GREY part
shows A
complement
28. PROPERTIES OF COMPLEMENTS
OF SETS
1) Complement laws :
1) A U A‟ = U
2) A ∩ A‟ = Φ
2) De Morgan‟s law : 1) ( A U B )‟ = A‟ ∩ B‟
2) ( A ∩ B )‟ = A‟ U B‟
3) Laws of double complementation : ( A‟ ) „ = A
4) Laws of empty set and universal set :
Φ „ = U & U‟ = Φ