A truth table is a mathematical table utilized in logic - more specifically—specifically in relation with Boolean algebra, boolean functions, and propositional calculus.
In detail and In very simple method That can any one understand.
If you read this all you doubts about function will be clear.
because i have used very simple example and simple English words that you can pick quickly concept about functions.
#inshallah.
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.
A truth table is a mathematical table utilized in logic - more specifically—specifically in relation with Boolean algebra, boolean functions, and propositional calculus.
In detail and In very simple method That can any one understand.
If you read this all you doubts about function will be clear.
because i have used very simple example and simple English words that you can pick quickly concept about functions.
#inshallah.
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.
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.
Relations and their Properties
CMSC 56 | Discrete Mathematical Structure for Computer Science
November 9, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
This will help you in illustrating operations on sets using Venn Diagram. Also, how to find the intersection, union, complement and difference of two sets.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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
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.
Relations and their Properties
CMSC 56 | Discrete Mathematical Structure for Computer Science
November 9, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
This will help you in illustrating operations on sets using Venn Diagram. Also, how to find the intersection, union, complement and difference of two sets.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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
Set theory is a monumental concept in the world of mathematics. Starting from business to even literature, set has uses in diverse fields. This pdf presents set in a unique and eye-catching way. Hope you guys enjoy it.
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.
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.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
2. SET
• A set is collection of well-defined objects.
• Each of the objects in the set is called an element of the set.
• Elements of a set are usually denoted by lower case letter (a, b, c …).
• While sets are denoted by capital letters (A, B, C …).
• The symbol ‘∈ (is belongs to)’ indicates the membership in a set. While the
symbol ‘∉ (is not belongs to)’ is used to indicate that an element is not in the
set.
• For example, if A = {1, 2, 3, a, b} then we can write that a ∈ A, 1 ∈ A but 4 ∉ A.
3. REPRESENTATION
Listing method :
• In listing method, all the elements of a set are listed, the elements are being separated by
commas and are enclosed within braces { }.
• For example, the set of all natural numbers less than 6 is described in listing method as :
{1, 2, 3, 4, 5}.
Property method :
• In property method, all the elements of a set possess a single common property which is not
possessed by any element outside the set.
• For example, the set of all natural number between 0 & 6 described in property method as:
{𝑥; 𝑥 𝑖𝑠 𝑎 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 & 0 < 𝑥 < 6}
5. • Subsets : Let A and B be two sets. If each elements of set A is an element of
set B then A is called subset of set B and it is denoted by 𝐴 ⊂ 𝐵
• Empty set (null set) does not contain any element and It is denoted as { } or
𝛟.
• A set which contain at least one element is called Non-empty set.
• A set which contain exactly one element is called Singleton set.
• A set which contain finite number of elements is called finite set.
SOME DEFINATIONS
6. SOME DEFINITIONS
• A set which contain infinite number of elements is called infinite set.
• Two set A and B are said to be equal if they have the same elements
and we write A=B. Otherwise, the sets are said to be unequal, and we
write A≠B.
• There always happens to be a set that contains all set under
consideration i.e., it is a super set of each of the given sets. Such a set
is called the universal set and is denoted by U.
• Remark: if A is a subset of B, then B is a superset of A.
7. OPERATIONS ON SET
• Union
Union of the sets A and B, denoted by A ∪ B, is the
set of distinct elements that belong to set A or set
B, or both.
• Intersection
The intersection of the sets A and B, denoted by A
∩ B, is the set of elements that belong to both A
and B i.e. set of the common elements in A and B.
8. OPERATIONS ON SET
• Disjoint
Two sets are said to be disjoint if their intersection
is the empty set. i.e, sets have no common
elements.
• Set Difference
The difference between sets is denoted by ‘A – B’,
which is the set containing elements that are in A
but not in B. i.e., all elements of A except the
element of B.
9. OPERATIONS ON SET
• Complement
The complement of a set A, denoted by
AC is the set of all the elements except the
elements in A. Complement of the set A
is U – A.
• A Delta B
The symmetric difference using Venn
diagram of two subsets A and B is a subset of
U, denoted by A △ B and is defined by :
A △ B = (A – B) ∪ (B – A)
10. SIZE OF SET
• Size of a set can be finite or infinite.
• For example:
Finite set: Set of natural numbers less than 100.
Infinite set: Set of real numbers.
• Size of the set S is known as Cardinality number, denoted as |S|.
• Example: Let A be a set of odd positive integers less than 10.
Solution : A = {1,3,5,7,9}, Cardinality of the set is 5, i.e.,|A| = 5.
• Note: Cardinality of a null set is 0.
11. POWER SET
• The power set is the set all possible subset of the set S.
Denoted by P(S).
• Example : What is the power set of {0,1,2}?
Solution : All possible subsets
{∅}, {0}, {1}, {2}, {0,1}, {0,2}, {1,2}, {0,1,2}.
• Note: Empty set and set itself is also the member of this set of subsets.
• Cardinality of power set is 2^n, where n is the number of elements in a set.
12. CARTESIAN PRODUCT
• Let A and B be two sets. Cartesian product of A and B is denoted by A × B, is
the set of all ordered pairs (a,b), where a belong to A and b belong to B.
A × B = {(a, b) | a ∈ A ∧ b ∈ B}.
• Example 1. What is Cartesian product of A = {1,2} and B = {p, q, r}.
Solution : A × B ={(1, p), (1, q), (1, r), (2, p), (2, q), (2, r) };
13. EXAMPLE
A survey asks 200 people “What beverage do you drink in the morning”,
and offers choices:
• Tea only
• Coffee only
• Both coffee and tea
Suppose 20 report tea only, 80 report coffee only, 40 report both. How
many people drink tea in the morning? How many people drink
neither tea or coffee?
14. SOLUTION
• This question can most easily be answered by creating a
Venn diagram. We can see that we can find the people
who drink tea by adding those who drink only tea to
those who drink both: 60 people.
• We can also see that those who drink neither are those
not contained in the any of the three other groupings, so
we can count those by subtracting from the cardinality of
the universal set, 200.
• 200 – 20 – 80 – 40 = 60 people who drink neither.