For Class 9th Mathematics in Pakistan, specifically for the 2025 academic year, “Sets & Functions” is a core topic and is typically covered as Chapter 3 in the new math textbooks published by the Punjab Curriculum and Textbook Board (PCTB).
Here’s a breakdown of what you can expect to find in the “Sets & Functions” chapter, based on the new 2025 curriculum:
9th New Math Chapter 3 Sets & Functions All Exercise Solution
For students in Class 9th in Pakistan, particularly those following the Punjab Curriculum and Textbook Board (PCTB) syllabus, “Sets & Functions” is a fundamental and crucial chapter in the new mathematics textbook for the 2025 academic year. It’s typically designated as Chapter 3.
This chapter introduces students to the foundational concepts of sets and their operations, and then builds upon this to introduce the basic ideas of relations and functions. Mastering these concepts is essential for higher-level mathematics.
Here’s a Class 9 New Maths, Chapter 3 Notes, All Exercises Solutions.
Also Read: Class 9 New Maths Full Book Solutions New Syllabus, Chapter Wise Solutions
Key Concepts Covered in “Sets & Functions”
The chapter is designed to cover the following core topics comprehensively:
- Introduction to Sets:
- Definition of a Set: What a set is, its elements, and how to define well-defined collections of objects.
- Representation of Sets:
- Descriptive Form: Describing the elements of a set using words.
- Tabular Form (Roster Form): Listing all the elements of a set within curly braces.
- Set-Builder Notation: Defining a set by specifying the properties its elements must satisfy.
- Types of Sets:
- Empty Set (Null Set/Void Set): A set containing no elements, denoted by ∅ or {}.
- Singleton Set: A set containing only one element.
- Finite and Infinite Sets: Sets with a countable and uncountable number of elements, respectively.
- Equal Sets: Sets containing exactly the same elements.
- Equivalent Sets: Sets having the same number of elements (cardinality).
- Subsets: A set A is a subset of set B if all elements of A are also elements of B (A⊆B).
- Proper and Improper Subsets: Distinguishing between subsets that are not equal to the original set (proper) and those that are (improper).
- Superset: If A is a subset of B, then B is a superset of A.
- Universal Set: The set containing all possible elements under consideration, denoted by U.
- Power Set: The set of all possible subsets of a given set.
- Operations on Sets:
- Union of Sets (A∪B): The set containing all elements that are in A, or in B, or in both.
- Intersection of Sets (A∩B): The set containing all elements that are common to both A and B.
- Difference of Sets (A−B or A∖B): The set containing all elements that are in A but not in B.
- Complement of a Set (A′ or Ac): The set of all elements in the universal set that are not in A.
- Venn Diagrams:
- Graphical representation of sets and their relationships, including set operations.
- Properties of Set Operations:
- Commutative Laws: A∪B=B∪A and A∩B=B∩A.
- Associative Laws: (A∪B)∪C=A∪(B∪C) and (A∩B)∩C=A∩(B∩C).
- Distributive Laws: A∪(B∩C)=(A∪B)∩(A∪C) and A∩(B∪C)=(A∩B)∪(A∩C).
- De Morgan’s Laws: (A∪B)′=A′∩B′ and (A∩B)′=A′∪B′.
- Binary Relations:
- Ordered Pairs: (a,b) where the order of elements matters.
- Cartesian Product of Two Sets (A×B): The set of all possible ordered pairs where the first element is from A and the second is from B.
- Definition of a Binary Relation: A subset of the Cartesian product of two sets.
- Domain and Range of a Relation: The set of all first elements and second elements in the ordered pairs of a relation, respectively.
- Functions:
- Definition of a Function: A special type of relation where each element in the domain is mapped to exactly one element in the codomain.
- Domain, Codomain, and Range of a Function:
- Domain: The set of all possible input values.
- Codomain: The set of all possible output values.
- Range: The actual set of output values produced by the function.
- Types of Functions:
- Into Function: Where the range is a proper subset of the codomain.
- One-One (Injective) Function: Each element in the domain maps to a unique element in the codomain.
- Onto (Surjective) Function: The range of the function is equal to its codomain.
- Bijective Function: A function that is both one-one and onto.
Changes in the New 2025 Edition
While the core concepts of sets and functions generally remain consistent, the new 2025 curriculum (which follows the Single National Curriculum or SNC in Pakistan) often involves:
- Revised Explanations: Simpler language and clearer examples to enhance understanding.
- Updated Examples and Exercises: New problems designed to align with the revised learning objectives and promote critical thinking.
- Focus on Conceptual Understanding: Emphasis on understanding why certain properties hold true, rather than just memorizing formulas.
- Real-world Applications: Potentially more examples and problems that relate sets and functions to everyday scenarios.
Students are encouraged to refer to the specific textbook published by the PCTB for the most accurate and detailed content for the 2025 academic year. Online resources, including YouTube channels and educational websites, are also providing comprehensive solutions and explanations for the new syllabus.
It’s great you’re looking for solutions to the “Sets & Functions” chapter (Chapter 3) of the new Class 9th Math Book for 2025! In Pakistan, especially for students under the Punjab Curriculum and Textbook Board (PCTB), the new curriculum often means revised exercises and a focus on conceptual understanding.
While I cannot provide an interactive, step-by-step solution for every problem in the textbook (as the specific problems can vary and a full textbook solution would be lengthy), I can guide you on where to find reliable solutions and how to approach them.
Where to Find Solutions:
- Online Educational Platforms:
- MathCity.org: This is a highly recommended resource for Pakistani students. They often provide detailed, step-by-step solutions for PCTB textbooks. You can typically find a section for “Solutions: Math 9th PCTB” where Chapter 3 (Sets & Functions) exercises (Exercise 3.1, 3.2, 3.3, and Review Exercise) are available for viewing online or download as PDFs.
- Scribd / Other Document Sharing Sites: You might find PDFs of solved exercises or complete notes uploaded by teachers or students. Search terms like “9th Math New Book 2025 Punjab Board Solutions Chapter 3” or “Class 9th Math PCTB Sets & Functions Solved Exercises.”
- YouTube Channels:
- Many educators in Pakistan are creating video lectures and solutions for the new 9th Class Math Book. These videos often go through each exercise question by question, explaining the concepts and steps.
- Look for channels with titles like:
- “9th Class Math New Book 2025 || Complete Solution || Punjab Text Book”
- “9Th Class Math New Book 2025 Exercise 3.1 || PCTB || National Curriculum of Pakistan”
- “Math 9th | New Book | Punjab Board | Chap 3 | Sets & Functions | Ex 3.1/3.2/3.3”
- Channels by “Sir Shahzad Sair,” “Maths by Kh.,” “SIR SADAM,” “Qais Ali Khan,” and “Hafsa study” are actively uploading solutions for the new 2025 book.
- Local Bookstores/Publishers:
- Many private publishers release “Key Books” or “Solution Guides” alongside the official PCTB textbooks. These books contain solved exercises. Visit local bookstores in Sargodha or inquire from your school’s booklist.
How to Approach Solutions Effectively:
- Understand the Concepts First: Before jumping to solutions, make sure you understand the theoretical concepts covered in Chapter 3, such as:
- What is a set? How are sets represented?
- Different types of sets (empty, finite, infinite, subset, universal, power set).
- Set operations (union, intersection, difference, complement).
- Venn Diagrams.
- Properties of set operations (De Morgan’s Laws, distributive laws, etc.).
- Binary relations and Cartesian product.
- Definition and types of functions (one-to-one, onto, bijective, into).
- Attempt Problems Yourself: The best way to learn is by doing. Try to solve the problems in the textbook exercises on your own first. Even if you get stuck, the effort helps you identify your weak areas.
- Refer to Solutions for Guidance:
- If you’re stuck, refer to the solution for that specific problem.
- Compare your approach with the provided solution.
- Understand the reasoning behind each step, rather than just copying.
- Use solutions to verify your answers.
- Practice Regularly: Mathematics requires consistent practice. Work through all the exercises in Chapter 3 to solidify your understanding.
Good luck with your studies!
Also Read: Class 9 New Maths Book Solution, Notes 2025 for Punjab Boards (BISEs)