What is a Relation

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/UP-LT-GRADE-ASSISTANT-TEACHER-2025/digital-logic-circuits-discrete-math-structures/relations/cartesian-product-relation-inverse-complement/asset-what-is-a-relation after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: 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
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography: Geography
  16. GS Paper | 02 | History: History
  17. GS Paper | 03 | Indian Economy & Social Development: Indian Economy
  18. GS Paper | 04 | General Science: Biology, Chemistry, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research
  19. GS Paper | 05 | Elementary Maths: संख्या पद्धति / Number System, Divisibility Rules, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, प्रतिशत / Percentage, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, समय और कार्य / Time and Work, समय, चाल और दूरी / Time, Speed and Distance, Algebra, घन क्षेत्रमिति / Solid Mensuration, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, Statistics, Probability, Sequence and Series (Series), मिश्रण और एलिगेशन / Mixture and Alligation, Calculus, Trigonometry, Vectors, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, यूक्लिडीय ज्यामिति और क्षेत्रमिति / Euclidean Geometry and Mensuration, सांख्यिकी और प्रायिकता / Statistics and Probability, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers, समतल क्षेत्रमिति / Plane Mensuration, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics
  20. GS Paper | 06 | Indian Polity and Governance: Polity
  21. GS Paper | 07 | Current Events: समसामयिकी / Current Affairs
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a foundational lecture on the concept of a "Relation" in set theory. The instructor defines a relation as any subset of the Cartesian product of two sets, A and B. He derives a formula for the total number of possible relations based on set cardinalities. The lesson moves from abstract definitions to concrete examples, enumerating all possible relations systematically. Finally, the instructor briefly introduces matrix representation and identifies the largest and smallest possible relations.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor starts by defining a relation on the slide: "Let A and B are sets then every possible subset of 'AxB' is called a relation from A to B." He explains that if set A has m elements and set B has n elements, the Cartesian product AxB contains m*n pairs. He draws a diagram with set A={a, b} and set B={1, 2, 3}, drawing red arrows from elements of A to elements of B to visualize the pairs. He writes "m" and "n" above the sets and "mn" above the arrows. He explains that for every single element (pair) in the Cartesian product, there are two choices: either it is present in the subset (relation) or it is not. This binary choice for each of the m*n elements leads to the total number of possible relations being 2 raised to the power of m*n, which he writes to fill the blank on the slide.

  2. 2:00 – 4:01 02:00-04:01

    To illustrate the concept, the instructor presents a specific example: "For E.g. if A = {a, b}, B = {1, 2}". He lists the Cartesian product AxB = {(a, 1), (a, 2), (b, 1), (b, 2)}. He then displays a large table with four columns corresponding to these four pairs. The rows contain binary values (0 or 1), representing the presence or absence of each pair in a specific relation. This table systematically lists all 16 possible subsets of AxB, demonstrating the 2^4 calculation. He then transitions to a new slide titled "Matrix Representation," showing a grid where rows are labeled x, y, z and columns 1, 2, 3, with cells containing pairs like (x,1). Finally, he states that the "Largest relation possible will be AxB" and leaves a blank for the "Smallest possible relation," which implies the empty set.

The lecture successfully connects the theoretical definition of a relation to practical calculation methods. By defining a relation as a subset of the Cartesian product, the instructor establishes that a relation is essentially a selection of pairs. The derivation of the 2^(m*n) formula is the central mathematical takeaway, highlighting the exponential growth of possible relations as set sizes increase. The detailed enumeration table for the example A={a,b}, B={1,2} serves as a concrete verification of the formula, showing exactly how the 16 combinations arise. The brief introduction to matrix representation and the identification of the largest and smallest relations provide a complete overview of the basic properties of relations, preparing students for more complex topics like equivalence relations or functions.

Loading lesson…