Total order relation

Duration: 2 min

This video lesson is available to enrolled students.

Inside: a video lesson and guided study material.

Module outline

About Course: About the Course
Paper 1 | General Studies: State Wise GK
Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
Paper 1 | Current Affairs: GK- Current Affairs
Paper 2 | Discrete Mathematical Structure: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Probability
Paper 2 | Digital Computer Organization And Architecture: Number System, Number Representation, Sequential Circuits, Combinational Circuit, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
Paper 2 | Data Structure And Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Advanced Algorithms
Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS
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, Complexity Theory
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
Paper 2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Enhanced Data Models
Paper 2 | Computer Network And Information Security: Introduction to CN, Data Communication, Application Layer, Hardware basics, Cyber Threats and Malware Attacks, Network Security, 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
Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
Paper 2 | Current Trends & Technologies: Emerging Tech Trends, Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms, Artificial Intelligence, Data Warehousing & Mining, Electronic Data Interchange and E-Commerce, Terms & Abbreviations
Paper 2 | Full Length Mock Tests:

AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture introduces the concept of a total order relation in discrete mathematics. The instructor defines it as a relation where every pair of elements is comparable, meaning for all a and b in set A, either (a,b) or (b,a) belongs to the relation R. Using a dark slide, the instructor contrasts two examples: A = {1, 2, 3, 6} under the divisibility relation is not a total order because some elements are incomparable, while A = {1, 2, 4, 8} is a total order. The instructor then hand-draws a green trapezoid on the board listing ordered pairs such as (1,1), (1,2), (1,4), (1,8), (2,2), (2,4), and (2,8) to illustrate the comparable pairs in the total order case. The slide also references partial ordering sets (Posets) with examples like [A, /], [A, <=], and (P(S), ⊆].

Chapters

0:00 – 1:31 00:00-01:31
The instructor presents a slide titled 'Total order relation' with the definition: every pair of elements are comparable i.e. either (a, b) or (b, a) ∈ R for ∀ a, b ∈ A. The slide shows the example 'A = {1, 2, 3, 6}, then Poset [A,/] is not a total order relation' with the bracketed part circled in green, and 'but A = {1,2,4,8} will be' with the set underlined in green. The instructor points to these lines and later draws a green trapezoid on the board listing ordered pairs (1,1), (1,2), (1,4), (1,8), (2,2), (2,4), and (2,8) to demonstrate the comparable pairs. The slide also lists 'Partial ordering set (Poset): [A, /], [A, <=], (P(S), ⊆]' as related context.

The central idea is the definition of a total order relation: every pair of elements in the set must be comparable under the relation. The instructor uses two contrasting examples to illustrate this: {1, 2, 3, 6} under divisibility fails because 3 and 6 are not comparable in the required way (actually 3 divides 6, but 2 and 3 are incomparable), while {1, 2, 4, 8} succeeds because every pair is comparable under divisibility. The hand-drawn trapezoid with ordered pairs provides a concrete visualization of the relation's structure. The connection to Posets is noted, as a total order is a special case of a partial order where comparability holds for all pairs.