Onto (Surjective Function)

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/ISRO/discrete-mathematics/functions/onto-surjective-function-definition-count-and-properties/asset-onto-surjective-function 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.

The video lecture explains "Onto" or "Surjective" functions. The instructor defines a surjective function f from set X to Y, stating that for every y in Y, there is at least one x in X such that f(x) = y. He clarifies x need not be unique. The lecture uses diagrams to illustrate onto vs non-onto functions. Key conditions for finite sets are derived, specifically that the cardinality of the co-domain must be less than or equal to the cardinality of the domain.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the definition: "A function f from a set X to a set Y is surjective... if for every element y in the co-domain Y of f, there is at least one element x in the domain X of f such that f(x) = y." He presents three diagrams. The first shows element 'A' unmapped, marked with a red cross as not onto. The second and third show all Y elements covered, marked with red ticks as onto. He writes "Range of f = B". Finally, he writes "If A and B are finite sets, then onto function from A->B is possible, |B| <= |A|" and circles it.

  2. 2:00 – 2:58 02:00-02:58

    The instructor elaborates on the cardinality condition. He writes |A| >= |B| to reinforce that the domain must have at least as many elements as the co-domain. He points to the third diagram where multiple elements map to the same target, showing onto functions don't require uniqueness. He concludes: "If |A| = |B|, then every onto function from A to B is also one-to-one function." This connects surjectivity with injectivity when set sizes are equal. He uses red annotations to track covered elements.

The lecture builds understanding of surjective functions from definition to application. It starts with the formal definition requiring every co-domain element to have a pre-image. It uses visual mapping diagrams to distinguish onto from non-onto functions, emphasizing "Range = Co-domain". The instructor derives a necessary condition for finite sets (|Domain| >= |Co-domain|) and links surjectivity to injectivity when set cardinalities are equal. This moves from abstract definition to concrete visual verification and theoretical implications.

Loading lesson…