Maharashtra Board Class 9 Maths Part I Chapter 1 Sets PDF Download

Sets

Some pictures are given below. It contains the group of things you know.

We use special word for each of the collection given above. In all the above examples we can clearly list the objects of that collection. We call the collection of such objects as a Set.

Now, observe the collection. Happy children in the village, Brilliant students of the class. In both the examples the words Happy and Brilliant are relative terms, because the exact meaning of these words to be happy and to be brilliant differ from person to person. Therefore, these collections are not sets.

See the examples given below and decide whether it is a set or not.

Days of a week

Months in a year

Brave children in the class

First 10 counting numbers

Strong forts of Maharashtra

Planets in our solar system

Let's Learn

Sets

If we can definitely and clearly decide the objects of a given collection then that collection is called a set.

Generally the name of the set is given using capital letters A, B, C, Z

The members or elements of the set are shown by using small letters a, b, c, ...

If a is an element of set A, then we write it as a ∈ A and if a is not an element of set A then we write a ∉ A.

Now let us observe the set of numbers.

N = {1, 2, 3, ...} is a set of natural numbers.

W = {0, 1, 2, 3, ...} is a set of whole numbers.

I = {..., -3, -2, -1, 0, 1, 2, ...} is a set of integers.

Q is a set of rational numbers.

R is a set of real numbers.

Methods Of Writing Sets

There are two methods of writing set.

Listing Method Or Roster Method

In this method, we write all the elements of a set in curly bracket. Each of the elements is written only once and separated by commas. The order of an element is not important but it is necessary to write all the elements of the set.

e.g. the set of odd numbers between 1 and 10, can be written as A = {3, 5, 7, 9} or A = {7, 3, 5, 9}

If an element comes more than once then it is customary to write that element only once. e.g. in the word remember the letters r, m, e are repeated more than once. So the set of letters of this word is written as A = {r, e, m, b}

Rule Method Or Set Builder Form

In this method, we do not write the list of elements but write the general element using variable followed by a vertical line or colon and write the property of the variable.

e.g. A = {x | x ∈ N, 1 < x < 10} and read as set A is the set of all x such that x is a natural number between 1 and 10.

Teacher's Note

A set means a clear group of things. Like a class is a set of students because we know exactly who is in the class.

Exam Trick

Remember: A set must be clear and exact. Happy people is NOT a set because happy is different for everyone. But even numbers IS a set because we know exactly what even numbers are.

Points To Remember

A set is a clear group of things with exact meaning.

Capital letters like A, B, C are used for set names.

Small letters like a, b, c are used for elements.

There are two ways to write a set: Listing method and Rule method.

In listing method we write all elements inside curly brackets like {1, 2, 3}.

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