Inverse of a Relation

Duration: 2 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. 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, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. 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
  10. 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. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
  15. Paper 2 - Full-length Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment focuses on the mathematical concept of the inverse of a relation within set theory. The instructor, Sanchit Jain Sir, defines the inverse of a relation R from set A to set B. The text states the inverse relation, denoted as R^-1, is a relation from B to A. The definition is R^-1 = {(b, a) | (a, b) ∈ R}, indicating swapped element order. The lecture transitions to a concrete example. The Cartesian product A×B is listed with six elements involving 'a', 'b' and numbers 1, 2, 3. A specific relation R is defined as a subset: R = {(a, 1), (a, 3), (b, 2)}. The instructor derives the inverse relation R^-1 by reversing the ordered pairs from R. He writes out the resulting set R^-1 = {(1, a), (3, a), (2, b)}. Finally, he establishes a property regarding cardinality, writing |R| = |R^-1|, demonstrating that the number of elements remains constant.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the definition of the inverse of a relation, R^-1, mapping from set B back to set A. He displays the formula R^-1 = {(b, a) | (a, b) ∈ R} and underlines key phrases like "from A to B" and "from B to A" to emphasize direction change. He sets up an example using the Cartesian product A×B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)} and a specific relation R = {(a, 1), (a, 3), (b, 2)}. He calculates the inverse by swapping elements in the ordered pairs of R, writing R^-1 = {(1, a), (3, a), (2, b)} on the screen. He underlines the elements of R to show which ones are being transformed.

  2. 2:00 – 2:09 02:00-02:09

    The instructor concludes the derivation of the inverse relation. He writes the cardinality comparison |R| = |R^-1| to show that the number of elements in the original relation equals the number of elements in the inverse relation. The final screen displays the completed set R^-1 = {(1, a), (3, a), (2, b)} alongside the instructor's branding, reinforcing the lesson's conclusion. He gestures to emphasize the equality of the sets' sizes.

The video provides a clear, step-by-step introduction to finding the inverse of a relation. It starts with the theoretical definition, emphasizing the reversal of domain and codomain. It then solidifies understanding through a worked example where specific ordered pairs are swapped. The lesson concludes by highlighting a fundamental property: the cardinality of a relation and its inverse are identical. This progression from definition to application to property verification offers a complete micro-lesson on the topic.

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