हिंदी
CISCEICSE ICSE Class 6
पाठ्यपुस्तक उत्तर९५२२
अवधारणा स्पष्टीकरण और वीडियो३०७
पाठ्यक्रम

Concept of Sets

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Topics

  • Introduction
  • Definition: Sets
  • Well-defined and Not Well-defined Sets
  • Elements of a Set and Notation
  • Properties of Sets
  • Examples
  • Real-Life Applications
  • Key Points Summary
CISCE: Class 6

Introduction

Have you ever grouped all your favourite comics, crayons of the same colour, or the red marbles from a box?

When you make a collection of similar things, you are creating a set in mathematics!

CISCE: Class 6

Definition: Set

A set is a well-defined collection of distinct objects or elements.

  • Example 1: A collection of books.
  • Example 2: A group of students
CISCE: Class 6

Well-defined and Not Well-defined Sets

Well-Defined Set:
A set is well-defined if it is clear which objects belong to the set and which do not.

  • Example 1: "Lovely Flowers" is not well-defined because "lovely" is subjective.
  • Example 2: "Red Flowers" is well-defined because the colour is clear.

Not a well-defined set:

  • A set of nice toys — “nice” can mean different things to different people.
CISCE: Class 6

Elements of a Set and Notation

Elements of a set:
The objects inside a set are called elements or members of that set.

  • A = {p, q, r, s, t}
  • Here, A is the set and p, q, r, s, and t are its elements.

Symbols used in set theory:

  1. "∈" means "belongs to" or "is an element of".
  2. "∉" means "does not belong to" or "is not an element of".

Example:

  • If p ∈ A, it means "p belongs to A".
CISCE: Class 6

Properties of Sets

  1. Order doesn't matter:
    {1, 2, 3} = {3, 2, 1}
  2. No repeated elements:
    {a, a, b} = {a, b}
  3. The elements of a set are written inside a pair of curly braces and separated by commas.
    Example: A = {1, 2, 3, 4}
  4. The set is represented by a capital letter.
    Example: Set A = {1, 2, 3}
  5. If the elements of a set are alphabets, these elements are written in small letters.
    Example: Set B = {a, b, c}
CISCE: Class 6

Examples

1. Set of letters of the word “MEERUT”

  • Set: {m, e, r, u, t}

2. Set of vowels in the word “MUSSOORIE”

  • Set: {u, o, i, e}

CISCE: Class 6

Real-Life Applications

  • Set of your friends who wear glasses.
  • Set of the months with 31 days: {January, March, May, July, August, October, December}
  • Set of books in your schoolbag.
CISCE: Class 6

Key Points Summary

Word Meaning
Set Group of things with a common property
Element Each thing in the set
Well-defined Everyone knows what is in the set
∈ “is an element of” or “belongs to”
∉ “is not an element of” or “does not belong to”

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