Number of Onto (Surjective are Possible)

Duration: 5 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/engineering-maths/functions/onto-surjective-function-definition-count-and-properties/asset-number-of-onto-surjective-are-possible 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 lecture focuses on the mathematical concept of counting surjective (onto) functions between two finite sets. The instructor begins by defining the problem of finding the number of onto functions from set A to set B, denoting their cardinalities as $|A| = m$ and $|B| = n$. He introduces the general formula derived from the Principle of Inclusion-Exclusion, which is essential for solving such combinatorial problems. The lecture then transitions to a practical application using a specific question from the GATE 2015 exam, demonstrating how to apply the formula to find the number of onto functions from set $X = \{1, 2, 3, 4\}$ to set $Y = \{a, b, c\}$. The instructor walks through the substitution of values and the step-by-step arithmetic calculation to arrive at the final answer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the topic by writing the question 'No of onto function possible from A to B = ?' on the screen. He defines the cardinality of the domain set A as $m$ and the codomain set B as $n$. He then displays the general formula for the number of onto functions: $n^m - {}^nC_1(n-1)^m + {}^nC_2(n-2)^m - {}^nC_3(n-3)^m + \dots + (-1)^n {}^nC_{n-1} 1^m$. This formula is presented as the standard method for calculating surjective functions when the size of the domain is greater than or equal to the size of the codomain.

  2. 2:00 – 4:45 02:00-04:45

    The instructor presents a specific problem from GATE 2015 asking for the number of onto functions from set $X = \{1, 2, 3, 4\}$ to set $Y = \{a, b, c\}$. He identifies $m=4$ and $n=3$ and substitutes these into the previously shown formula. The calculation is written out as $3^4 - {}^3C_1(3-1)^4 + {}^3C_2(3-2)^4 - {}^3C_3(3-3)^4$. He simplifies this to $81 - 3(16) + 3(1)$, performing the arithmetic to get $81 - 48 + 3$, which equals 36. He circles the final answer 36 on the screen to conclude the example.

The video provides a clear pedagogical progression from theory to practice. It starts by establishing the theoretical framework for counting onto functions using the Principle of Inclusion-Exclusion, providing a reusable formula for students. It then immediately reinforces this theory by solving a concrete, exam-style problem. By breaking down the substitution of $m=4$ and $n=3$ into the formula and showing the detailed arithmetic, the instructor ensures students understand not just the formula itself, but also the mechanics of applying it correctly to find the number of surjective mappings between sets of different sizes.

Loading lesson…