RS Aggarwal Class 11 Solutions Chapter-1 Sets

RS Aggarwal Solutions Class 11 Maths Sets are based on the concepts of Parallelogram. Some of the key topics discussed in this chapter are:

• Sets 

The collection of objects or elements and it does not change from person to person is represented as a set. 

• Elements of a Set

Let us take an example:

C = {1, 2, 3, 4, 5 }

Since a set is mostly represented by the capital letter and the elements are represented as small letters.  Thus, C is the set and 1, 2, 3, 4, 5 are the elements of the set.

. The cardinal number of the set is 5. 

• Order of Sets

The number of elements of the set is the order of a set. The order of sets is also referred to as cardinality. 

Representation of Sets

Curly braces are used to represent the sets {}. For instance, {2,3,4} or {a,b,c} or {Bat, Ball, Wickets}. The elements in the sets are represented in either the Statement form, Set Builder Form or Roster Form. 

1. Statement Form - In statement form, the elements of a set are represented in a statement form and put in the curly brackets. For example, the set of odd numbers is less than 10.

2. Roster Form - In Roster form, all the members or elements of a set are listed. For example, the set of whole numbers is less than 8.

Natural Number = 0,1, 2, 3, 4, 5, 6, 7, 8,……….

Natural Number less than 8 = 0,1, 2, 3, 4,5,6,7,8

Therefore, the set is N = { 0,1, 2, 3, 4,5,6,7 .

3. Set Builder Form - The general form is, B = { x : property }

Example: Write the following sets in set builder form: B={3, 6, 9}

Solution:

3 = 3 x 1

6 = 2 x 3

9 = 3 X 3 

So, the set builder form is B = {x: x=3n, n ∈ N and 1  ≤ n ≤ 3}

Types of Sets

1. Empty Set - A set that does not contain any element is called an empty set or void set or null set. It is denoted by { } or Ø.

2. Singleton Set - A set that contains a single element. 

3. Finite Set- A set that has a definite number of elements. 

4. Infinite Set - A set that has no finite number of elements.  

5. Equivalent Set - Equivalent sets are called when the number of elements is the same in two different sets. 

6. Equal Sets - The two sets are said to be equal if they consist of exactly the same elements. 

7. Disjoint Sets - The two sets are to be disjoint if the set does not consist of any common element.

8. Subsets - A set ‘P’ is a subset of P if each element of P is also an element of Q. 

9. Proper Subset - If P⊆ Q and P ≠ Q, then P is called the proper subset of Q and it can be written as P⊂Q.Example: If P = {2,4,6} is  a subset of Q = {2,4,6} then it is not a proper subset of Q = {2,4,6 }

But, AP= {2,4} is a subset of Q = {2,4,6} and is a proper subset also.

10. Superset - If set P is a subset of set Q and then each element of set Q is present in set P, then P is a superset of set Q. 

11. Universal Set - A universal set is a kind of set which consists of all the sets according to a certain condition. It is said to be the set of all the possible values. 

Operations on Sets

 The Basic Operations On Sets Are:

1. Union of sets

2. Intersection of sets

3. A complement of a set

4. Cartesian product of sets.

5. Set difference

1. Union of Sets

If set P and set Q are two sets, then P union Q will be set having all the elements of set P and set Q. It is denoted as P∪ Q.

Example: Set A = {1,2,3} and B = {4,5,6}, then A union B is:

A ∪ B = {1,2,3,4,5,6}

2. Intersection of Sets

If set P and set Q are two sets, then P intersection Q is the set that consists of only the common elements between set P and set Q. It is denoted as P ∩ Q.

Example: Set P = {1,2,3} and Q = {4,5,6}, then P intersection Q is:

P ∩ Q = { } or Ø

3. Complement of Sets

The complement of any set, say A, is the set of all elements in the universal set which are absent from set A.  It is represented by A’.

4. Cartesian Product of Sets

If set P and set Q are two sets then the cartesian product of set P and set Q is a set of all ordered pairs (p,q), such that a is an element of P and Q is an element of Q. It is denoted by P X Q. 

We can represent it in set-builder form, such as:

A × B = {(a, b) : a ∈ A and b ∈ B}

Example: set A = {1,2,3} and set B = {Red, White}, then;

A × B = {(1,Red),(1,White),(2 Red),(2,White),(3,Red),(3,White)}

5. Difference of Sets

If set P and set Q are two sets, then set A difference set B will be the set that consists of elements of A but no elements of B. It is denoted as A – B.

Example: P = {1,2,3} and Q = {2,3,4}

P - Q  = {1} 

Preparation Tips for Class 11 Maths Rs Aggarwal Solutions

• Use the visual representation as in the Venn diagram for understanding Sets. 

• Understand the examples for a better understanding of properties and types of sets of RS Aggarwal Class 11 Chapter 1 solution.

• you should practice enough on this topic using class 11 maths RS Aggarwal solutions to score better. 

RS Aggarwal Class 11 Solutions Chapter-1 Sets include overall critical problem-solving skills which are ultimately needed to build a strong foundation in maths for all those candidates who are interested in pursuing professional courses abroad. The syllabus that is followed in RS Aggarwal Class 11 Solutions Chapter-1 Sets is strictly based on the CBSE class 11 book and hence gives overall guidance for Chapter 1 of Class 11. This chapter is a part of higher class mathematics and is also considered to be one of the important topics. The RS Aggarwal Class 11 Solutions Chapter-1 Sets helps solve difficult questions also which are important in entrance examinations like JEE Main and other such exams.