Class 9 Math Chapter 3: All Notes & Resources
Choose a resource below for Chapter 3 Sets and Functions, from solved exercises to definitions and MCQs.
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Class 9 Mathematics Chapter 3 introduces the fundamental concepts of sets, relations, and functions. You will explore set notations, perform operations like union, intersection, and difference, and represent these relationships using Venn diagrams. This hub gathers every Chapter 3 resource in one place. Start with the Chapter 3 definitions for quick revision, then move to the solved exercises below. For targeted practice, try the Chapter 3 MCQs. You can also review the Grade 9 Math Pairing Scheme to understand paper weightings. When you are done, return to the main Class 9 Mathematics page for the next chapter.
Last updated: October 22, 2026
Exercise 3.1 Solved
Write sets in set-builder and tabular forms, identify proper subsets, and calculate the number of elements in power sets.
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Exercise 3.2 Solved
Perform set operations including union and intersection, draw Venn diagrams, verify De Morgan's laws, and solve word problems using the Inclusion-Exclusion Principle.
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Exercise 3.3 Solved
Determine domains and ranges of relations, identify functions from mapping diagrams, and evaluate function values for given inputs.
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Review Exercise 3
Comprehensive mixed problems covering the entire chapter, including set equalities, Venn diagram proofs, and complex function evaluations.
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Chapter 3 Definitions
All 34 key definitions and formulas, covering sets, subsets, power sets, Venn diagrams, Cartesian products, relations, and function types.
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Chapter 3 MCQs
Multiple-choice questions covering the entire chapter with detailed solutions, perfect for exam preparation and self-testing.
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Muhammad Tayyab
Subject Specialist Math
MSc Mathematics Β· Govt Christian High School Daska, Sialkot, Punjab
Last updated: October 22, 2026
Key Concepts β Sets and Functions
Union of Sets
\(A \cup B\)
The set of all elements that belong to either \(A\) or \(B\) (or both).
Intersection of Sets
\(A \cap B\)
The set of elements that are common to both \(A\) and \(B\).
Difference of Sets
\(A - B\)
Elements that belong to \(A\) but not to \(B\).
Inclusion-Exclusion
\(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)
A formula to find the number of elements in the union of two sets without double-counting.
Cartesian Product
\(A \times B = \{(x, y) \mid x \in A \land y \in B\}\)
The set of all ordered pairs where the first element is from \(A\) and the second from \(B\).
Function Mapping
\(f: A \to B\)
A relation where every element in domain \(A\) maps to exactly one element in co-domain \(B\).
Chapter 3 Frequently Asked Questions
What is a set?
A set is a well-defined collection of distinct objects, numbers, or elements. For example, the set of vowels in English is \(\{a, e, i, o, u\}\).
What is the difference between a subset and a proper subset?
If every element of set \(A\) is in set \(B\), then \(A\) is a subset of \(B\). It is a "proper subset" if \(B\) contains at least one element that is not in \(A\) (meaning \(A \neq B\)).
What is the Cartesian product of two sets?
The Cartesian product \(A \times B\) is the set of all possible ordered pairs \((x, y)\) where \(x\) is from \(A\) and \(y\) is from \(B\).
How do you know if a relation is a function?
A relation is a function if every input (first element of the ordered pair) maps to exactly one output. No x-value can be repeated with a different y-value.
What is an onto function (surjective function)?
An onto function is a function where the range is equal to the co-domain. In other words, every element in the co-domain is the image of at least one element in the domain.
Created by Hira Science Academy | Aligned with Punjab Board 2027 Syllabus