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Sets — Revision Notes

Maharashtra Board · Class 9 · Mathematics

Sets revision notes for Maharashtra Board Class 9 Mathematics: 4 topics in quick points. Part of the Maharashtra Board Class 9 Mathematics syllabus.

59 questions24 flashcards5 concepts

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Key Topics to Revise

1

Introduction to Sets and Methods of Representation

  • A set is a well-defined collection of objects. The objects must be clearly identifiable — no ambiguity allowed.
  • Collections like 'happy children' or 'brilliant students' are NOT sets because the terms 'happy' and 'brilliant' are relative and differ from person to person.
  • Collections like 'days of a week', 'planets in our solar system', 'first 10 natural numbers' ARE sets because membership is clearly defined.
2

Types of Sets

  • Singleton Set: A set with exactly ONE element. Example: A = {2} (set of even prime numbers).
  • Empty Set / Null Set: A set with NO elements. Represented by {} or φ (phi). Example: Set of natural numbers between 2 and 3 = φ.
  • Finite Set: A set where the number of elements can be counted (including the empty set). Example: C = {4, 8, 12, 16, 20}.
3

Equal Sets, Subsets, and Venn Diagrams

  • Equal Sets: Two sets A and B are equal (A = B) if they have EXACTLY the same elements — order does not matter.
  • If even ONE element is different, the sets are NOT equal (A ≠ B).
  • Example: A = {l,i,s,t,e,n} and B = {s,i,l,e,n,t} → A = B (same elements, different order).
4

Universal Set and Complement of a Set

  • Universal Set (U): The larger set that contains all the sets under consideration as subsets. Every set in a problem is a subset of U.
  • The Universal set depends on the context of the problem. For example, if we study sets of numbers, U could be the set of all integers.
  • In Venn diagrams, the Universal set is represented by a RECTANGLE.

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Full Notes

Key Concepts

A set is a wellElements are the individual objectsIn the listing methodIn the rule methodAn empty set (or null set)

Frequently Asked Questions

What are the important topics in Sets for Maharashtra Board Class 9 Mathematics?
Key topics in Sets include Introduction to Sets and Methods of Representation, Types of Sets, Equal Sets, Subsets, and Venn Diagrams, Universal Set and Complement of a Set. Study these first, then practise questions on each for Class 9 exams.
How should I revise Sets for Class 9 exams?
Learn the core ideas first, then work through the 59 practice questions on Sets. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Sets

All Maharashtra Board Class 9 Mathematics Revision Notes

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