De Morgan's Law

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/ISRO/digital-electronics/dig-sys-boolean-basics/digital-fundamentals-boolean-algebra/asset-de-morgans-law after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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 Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, 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, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: 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, 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: 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, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This short lecture segment introduces De Morgan's Laws in propositional logic, using a digital whiteboard slide titled “De-Morgan's Laws.” The instructor presents the two core equivalences: ¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q), each supported by a four-row truth table with P and Q columns showing T/F combinations. Above the laws, an example sentence is given: “If I work hard but there are no vacancies, I won't get the job,” formalized as (P ∧ Q) ⇒ ¬R. The instructor then uses a pen/annotation tool to write out the negation of a conjunction, ¬(P ∧ Q), and transforms it into its equivalent form, ¬P ∨ ¬Q. Next, the negation of a disjunction, ¬(P ∨ Q), is written and transformed into ¬P ∧ ¬Q. The slide also includes a definition of logical equivalence: “Two sentences α and β are logically equivalent if they are true in the same set of models.” The teaching flow moves from stating the laws, to verifying them with truth tables, to demonstrating step-by-step transformations on the board, and finally connecting symbolic logic to Boolean algebra notation.

Chapters

  1. 0:00 – 1:37 00:00-01:37

    The slide displays “De-Morgan's Laws” with the two equivalences ¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q), each followed by a four-row truth table. An example sentence, “If I work hard but there are no vacancies, I won't get the job. (P ∧ Q) ⇒ ¬R,” appears above the laws. The instructor writes ¬(P ∧ Q), boxes it, and derives ¬P ∨ ¬Q; then writes ¬(P ∨ Q) and derives ¬P ∧ ¬Q. The definition “Two sentences α and β are logically equivalent if they are true in the same set of models” is also shown, linking the transformations to logical equivalence and Boolean algebra notation.

The central idea is that De Morgan's Laws provide equivalences between negated conjunctions/disjunctions and their dual forms. The instructor uses truth tables to verify these equivalences and then demonstrates the transformations step-by-step with handwritten annotations. The example sentence grounds the abstract logic in a real-world conditional statement, while the definition of logical equivalence clarifies that two formulas are equivalent when they share the same truth conditions across all models. The progression from printed laws to handwritten derivations helps students see both the formal rule and its practical application.

Loading lesson…