24.5 Practice Question

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/engineering-maths/relations/bounded-unbounded-distributive-complemented-lattices-and-boolean-algebr/asset-245-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.

This lecture segment analyzes a Hasse diagram to determine which subsets form a lattice. The instructor evaluates the full set and specific subsets by checking for unique least upper bounds (join) and greatest lower bounds (meet). He demonstrates that the full set fails this property because elements d and e lack a unique join or meet. Subsequently, he draws smaller Hasse diagrams for subsets {a, b, c, d}, {b, c, d, e}, and {a, b, c, e} to verify if they satisfy the lattice definition.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by analyzing the full Hasse diagram to test if it is a lattice. He writes 'd v e = ?' and 'd ∧ e = ?', indicating he is checking for the existence of a unique least upper bound (join) and greatest lower bound (meet). He marks option (a) as incorrect because elements d and e do not have a unique join or meet, proving the full set is not a lattice. He then proceeds to evaluate subsets {a, b, c, d}, {b, c, d, e}, and {a, b, c, e} by drawing smaller Hasse diagrams for each to visualize the relationships and verify if they satisfy the lattice property.

  2. 2:00 – 2:06 02:00-02:06

    The instructor concludes the analysis by marking the correct option based on his evaluation of the subset diagrams. He uses handwritten checks and crosses next to the options to indicate which subsets form a lattice. The final decision is based on whether each subset possesses unique joins and meets for all pairs of elements within that specific subset.

The core concept taught is the definition of a lattice in order theory, requiring every pair of elements to have a unique supremum (join) and infimum (meet). The instructor uses a counter-example with elements d and e to disprove the lattice property for the full set. He then applies this definition to subsets, demonstrating that removing problematic elements can result in a valid lattice structure. This method highlights the importance of verifying bounds for all pairs within a given set.

Loading lesson…