Equivalence class practice question

Duration: 1 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/engineering-maths/relations/equivalence-relation-equivalence-classes-partitions-of-a-set/asset-equivalence-class-practice-question 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.

The lesson presents a discrete mathematics practice question on equivalence relations and partitions. The instructor states that A = {1, 2, 3, 4, 5} has partitions {1, 4} and {2, 3, 5}, then asks for the equivalence relation from which these partitions are created. The method shown is to build the relation by listing ordered pairs inside each block of the partition: elements in the same part are related to one another, including reflexive pairs. For {1, 4}, the visible construction begins with pairs such as (1,1), (1,4), (4,1), and (4,4); for {2, 3, 5}, it continues with pairs among 2, 3, and 5. The instructional point is that a partition determines an equivalence relation whose classes are exactly the given blocks, so the answer should contain all ordered pairs needed to make each block closed under reflexivity, symmetry, and transitivity.

Chapters

  1. 0:00 – 1:00 00:00-01:00

    This one-minute window presents an equivalence-class practice question. The on-screen prompt states: “Let A = {1, 2, 3, 4, 5} is a set having partitions as {1, 4}, {2, 3, 5}.” It asks for the equivalence relation from which these partitions are created. The instructor writes the set and its two blocks on the board, then begins constructing the relation by listing ordered pairs inside each block. The first block {1, 4} yields pairs (1,1), (1,4), (4,1), and (4,4). The second block {2,3,5} yields pairs among 2, 3, and 5. The lesson emphasizes that an equivalence relation is the union of all ordered pairs whose elements lie in the same partition block.

Teaching progression: first identify the set and partition blocks; second translate each block into ordered pairs; third combine those pairs to form the full relation. This segment can answer doubts such as why (1,4) and (4,1) both appear, why reflexive pairs like (2,2), (3,3), and (5,5) are required, why no pair such as (1,2) is included, and how to verify reflexivity, symmetry, and transitivity from the partition. The expected answer is the union of all pairs inside {1, 4} and all pairs inside {2, 3, 5}, not merely the non-reflexive cross-pairs.

Loading lesson…