Partial order example

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/DSSSB-TGT-COMPUTER-SCIENCE-PAPER-2/mathematics-i-ii-iii-iv/relations/partial-order-relation-properties-partially-ordered-set-poset-and-total-order-relation/asset-partial-order-example after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  3. Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Cloud Computing, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  4. Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  5. Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  6. Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  7. Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  8. Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  9. Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep
  10. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  11. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  12. Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  13. Mathematics - I, II, III, IV: Permutation and Combination, Logarithm, Linear Algebra, Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory
  14. Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  15. Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  16. Statistical Techniques: Probability, Statistics
  17. Interpolation - DI: Data Interpretation
  18. Basis of Physics: Physics
  19. Previous Year Paper:
  20. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces partial ordering sets (Posets) and demonstrates how to construct the relation for a specific example. The instructor begins by defining a Poset as a set A with a partial order relation R, denoted [A, R]. Examples of Posets include [A, /] for divisibility, [A, <=] for less-than-or-equal-to, and [P(S), ⊆] for subset relations. The main worked example uses the set A = {1, 2, 3, 6} with the divisibility relation. The instructor defines (a,b) ∈ R if a divides b, which is equivalent to b/a being an integer in A. The instructor then explicitly lists the ordered pairs that satisfy this condition: (1,2), (1,3), (1,6), (2,6), (3,6), and (6,6). These pairs are circled to highlight the complete relation. The lecture focuses on translating an abstract definition into a concrete set of ordered pairs, showing how the divisibility rule generates each pair in the relation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The slide titled 'Partial ordering set (Poset)' defines a Poset as a set A with a partial order relation R, denoted [A, R]. Examples listed include [A, /], [A, <=], and [P(S), ⊆]. The instructor selects the divisibility example and writes A = {1, 2, 3, 6} in green chalk. The condition (a,b) ∈ R is defined as b/a ∈ A, meaning a divides b. The instructor begins listing ordered pairs such as (1,2), (1,3), and (1,6) to show how the relation is constructed from the set elements.

  2. 2:00 – 3:33 02:00-03:33

    The instructor completes the list of ordered pairs for the divisibility relation on A = {1, 2, 3, 6}, adding (2,6), (3,6), and (6,6). The full set of pairs is enclosed in a large green oval to emphasize the complete relation. A fraction 24/12 appears on the right side of the board, possibly as an additional illustration. The lecture concludes by showing how the abstract definition (a,b) ∈ R if a divides b translates into a concrete set of ordered pairs, reinforcing the connection between the rule and its explicit enumeration.

The lecture teaches how to construct a partial ordering set (Poset) by defining the relation explicitly. The key concept is that a Poset [A, R] consists of a set A and a relation R that satisfies partial order properties. The worked example uses divisibility on {1, 2, 3, 6}, where (a,b) ∈ R means a divides b. The instructor demonstrates the method by checking each pair of elements to see if one divides the other, producing the relation {(1,2), (1,3), (1,6), (2,6), (3,6), (6,6)}. This approach helps students understand how to move from an abstract definition to a concrete representation of the relation. The circling of the pairs emphasizes that this complete set constitutes the relation R for the given Poset.

Loading lesson…