Practice Questions

Duration: 7 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/engineering-maths/propositional-and-predicate-logic/implication-and-bi-conditional-operators-in-logic/asset-practice-questions-2352 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 educational video features a lecture on propositional logic, specifically focusing on determining the validity of logical arguments. The instructor, Sanchit Jain, systematically evaluates seven distinct arguments presented in tabular format. He applies standard rules of inference such as Hypothetical Syllogism, Constructive Dilemma, and Modus Tollens. He also discusses the Principle of Explosion regarding contradictory premises. The session aims to help students distinguish between valid and invalid logical structures.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture begins with Argument 1, consisting of premises p->q and q->r, concluding p->r. The instructor marks this valid, identifying it as Hypothetical Syllogism. He then analyzes Argument 2, with premises p v q, p->r, and q->r, concluding r. He marks this valid, explaining it as a case analysis where both options lead to r. Next, he examines Argument 3: p v q, p->r, q->s, concluding r v s. He marks this valid as Constructive Dilemma. Finally, he introduces Argument 4: p->r, q->s, ~r v ~s, concluding ~p v ~q. He begins to analyze the structure of this final argument in the first section.

  2. 2:00 – 5:00 02:00-05:00

    The instructor elaborates on Argument 4, writing down the logical equivalence of ~r v ~s to ~(r ^ s). He explains that if the consequents are false, the antecedents must be false, making the argument valid. He then moves to Argument 5: premises p and q, concluding r. He marks this invalid, noting that 'r' is a new variable with no logical connection to the premises. He proceeds to Argument 6: premises p and ~p, concluding q. He marks this valid, explaining that contradictory premises (p and ~p) imply any conclusion, a concept known as the Principle of Explosion or Ex Falso Quodlibet. He writes out the implication (p ^ ~p) -> q to demonstrate the logic.

  3. 5:00 – 6:30 05:00-06:30

    The instructor briefly addresses Argument 7, which has an empty premise P1 and concludes q. He marks this invalid, stating that a conclusion cannot be derived from no premises. He summarizes the key takeaways, emphasizing that validity is about the form of the argument. He concludes the lecture by reinforcing the importance of checking logical structure over content truth. He ensures students understand that even if premises are false, the argument can still be valid if the structure holds.

The video provides a comprehensive review of logical validity through seven examples. It covers standard inference rules like Hypothetical Syllogism and Constructive Dilemma. It also highlights edge cases like the Principle of Explosion where contradictory premises make an argument valid regardless of the conclusion. The instructor uses visual aids like checkmarks and crosses to indicate validity, helping students quickly grasp the correct logical forms. The session effectively bridges theoretical rules with practical application on the board, ensuring students can identify valid structures in complex scenarios.

Loading lesson…