13. SETS
Indiviual object in the set is called ELEMENT or a
MEMBER of the set.
Sets are denoted by capital alphabets , e.g. A, B, C etc.
Elements of set are denoted by small alphabets , e.g. a,
b, c etc.
If a is an element of set X then we write it as a Є X
If a is not an element of set X, then it is written as a Є X
15. Types of Sets
Empty set : it’s a set having no element. Also known as
Null set, it is denoted by Ф
Singleton set : it’s a set having only one element
Finite set : it’s a set wherein counting of elements ends
at a certain stage
Infinite set : it’s a set in which counting of elements do
not end at any stage
An empty set is a finite set
Natural and whole numbers, integers, rational and real
numbers are infinite sets
16. Few concepts worth remembering
Natural and Whole numbers
these includes numbers like 1,2,3,4 etc
only difference is we include ‘0’ (zero) in whole
numbers but not in natural numbers
are not fractions, decimals or negative numbers
Integers
are positive or negative numbers and includes zero
are whole numbers but can be negative too
17. Few concepts worth remembering
Rational numbers
Includes integers, fractions and repeating decimals
• Irrational numbers
Includes only decimals that have no pattern and continue
forever
• Real numbers
It includes every thing discussed above
19. Methods of writing sets
Listing method (Roster form)
Rule method (Set builder form)
Examples
1. Set of first 20 even natural numbers
Roster form
A = {2, 4, 6, 8, ………40}
Set builder form
A = {x|x is even natural number, 2 ≤ x ≤ 40}
20. Examples
Example 2
Set of first 10 multiples of 5
Roster form
A = {5, 10, 15, 20, …..50}
Set builder form
A = {x|x=5n, n Є N, 1 ≤ n ≤ 10}
21. Concept of Subsets
If every element of set B is an element of set A, then
set B is subset of set A
Subset can be proper subset or improper subset
If set B is subset of set A and set A contains at least one
element which is not in set B, then set B is proper
subset of set A
If set A is subset of set B and if set B is subset of set A,
then they are improper subsets of each other
B A is to be read as set B is proper subset of set A
22. Concepts of subsets
A B is to be read as set A is super set of set B
A B is to be read as set A is improper subset of set
B
Every set is subset of itself
Empty set is subset of every set
23. Universal set
A non-empty set of which all the sets under
consideration are the subsets of that set is called
universal set
It is denoted by ‘U’