A well defined collection of objects are known as sets. This is a fundamental part of mathematics in the present day. Sets are used to define the concepts of relations and functions. They are used for the study of geometry, probability, sequences etc. Mathematical problems become clearer and easy to understand due to application of sets. They become a powerful building block of maths.This is a very important chapter in maths for 11th standard students of CBSE Board. Solutions to all the questions in this chapter can be easily found in any good solution key that provides NCERT Solutions for Class 11 Maths. In day to day life there are several collections of objects such as groups of people, a football team, pack of cards etc. but similarly we come across in mathematics also such as natural numbers, prime numbers etc. 

Representation of sets 

The collections of sets can be examined in following ways:

N : the set of all natural numbers 

Z : the set of all integers 

Q : the set of all rational numbers

 R : the set of real numbers 

Z+ : the set of positive integers 

Q+ : the set of positive rational numbers, and

 R+ : the set of positive real numbers

There are few points to be noted in the sets for example,

1. Objects, elements and members are synonyms terms of sets. 
2. Sets are denoted by capital letters such as A,B,C,D etc
3. The elements are denoted by small letters such as a,b,c,d etc

Let’s discuss with an example, If a is an element of set A, In mathematics, we say  “a belongs to A”. here “belongs to” is denoted by epsilon ∈ . Thus it is “a ∈ A”. If b is not an element of set A then it is denoted as “b  ∉ A”.

There are two methods to represent the sets 

1. Roster or tabular form: all the elements in the sets are separated by comma, and enclosed within the brackets, For example, 

• the set of all natural numbers is 20 (1,2,3,4,5,5)
• The set of vowels in english alphabets (a,e,i,o,u)

2. In set builder form: all the elements have a common property which does not have any element outside the set. 

There are different types of sets

1. Empty sets: are those which do not contain elements. The empty set is denoted by a symbol  φ or { }. 
2. Finite and infinite sets: are those which consist of empty or definite number of elements. For example, W is the set of the week then W is finite
3. Equal sets: are those which consist of the same elements. For example A and B have the same elements. It will be A = B, and if it is unequal then it will be A  ≠ B.
4. Subsets: if set A is said to be set of B if element A is similar to element B. It is denoted by a symbol ⊂. 
5. Power set: the collection of all subset of set A is called as power set of A. It is denoted by P(A)
6. Universal set: the set of all even numbers are called a universal set. It is denoted by U.

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Summary

Straight lines is a very important chapter in Maths for 11th standard students of CBSE Board in India. This article gives an overview of straight lines and its types.