Partial order example

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/engineering-maths/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. Paper-2 | Programming & Data Structures: 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
  3. Paper-2 | Databases / DBMS & SQL: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics, Network Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. Paper-2 | Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. Paper-2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
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…