Question

My question is - Explain sets and it's Types . Also give some important formula of sets class 11 Chapter plss

Answer 1

Heya !
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★Sets★
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→ What is a set ?
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=> A set is a collection of well defined and different objects . Here we need to remember two basic words .

• Well defined - it signifies that there must be a rule given according to which we can identify if a particular element belongs to a set or not.

• Different - it signifies that repetition isn't allowed in a set .

=> A set is denoted by a capital letter in curly brackets . For Example , 

A = { 1 , 2 , 3 } 

→ Ways of Representing a Set : 
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1. Roaster Method - in this we simply mention the elements .

Ex. A = { 1 , 2 , 3 , 4 } 

2. Set Builder Method - in this we specify some rule / condition to make the set .

Ex. A = { x : 0< x < 5 }

→Types of Set 
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•Void / Empty Set : has no elements.

•Singleton Set : has only a single element .

•Finite Set : has a Finite number of elements .

•Infinite Set : has infinite elements.

→Some Basic Formulas : 
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1. A U B = N ( A ) + N ( B ) + N ( A n B )

2. A U B = N ( A ) + N ( B ) [ for disjoint sets ] 

3. A U B U C = N( A ) + N( B ) + N ( C ) - N ( A n B ) - N ( B n C ) - N ( C n A ) + N ( A n B n C )

[ Note : here U means the Union and n means the intersection of a set . ] 

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Answer 2

Definition

A set is a collection of objects.

It is usually represented in flower braces.

For example:
Set of natural numbers           = {1,2,3,…..}
Set of whole numbers             = {0,1,2,3,…..}

Each object is called an element of the set.

The set that contains all the elements of a given collection is called the universal set and is represented by the symbol ‘µ’, pronounced as ‘mu’.

For two sets A and B,

n(AᴜB) is the number of elements present in either of the sets A or B.n(A∩B) is the number of elements present in both the sets A and B.n(AᴜB) = n(A) + (n(B) – n(A∩B)

For three sets A, B and C,

n(AᴜBᴜC) = n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(C∩A) + n(A∩B∩C)

 

Consider the following example:

Question: In a class of 100 students, 35 like science and 45 like math. 10 like both. How many like either of them and how many like neither?

Solution:

Total number of students, n(µ) = 100

Number of science students, n(S) = 35

Number of math students, n(M) = 45

Number of students who like both, n(M∩S) = 10

Number of students who like either of them,

n(MᴜS) = n(M) + n(S) – n(M∩S)

→ 45+35-10 = 70

Number of students who like neither = n(µ) – n(MᴜS) = 100 – 70 = 30