Sets
Beginner level
WHAT are SETS?
A set is a collection of well-defined and well distinguished objects
of our perception or thought.
– Example: A = {1, 2, 3, 4, 5}
What is an ELEMENT of a SET?
The objects in a set are called its elements.
So in case of the above Set A,
The elements would be 1, 2, 3, 4, and 5.
We can say, 1 ∈ A, 2 ∈ A etc.
Usually we denote Sets by capital letters like A, B, C, etc, while their
elements are denoted in small letters like x, y, z etc.
Note:-
If x is an element of A, then we say x belongs to A and we represent
it as x ∈ A.
If x is not an element of A, then we say that x does not belong to A
and we represent it as x ∉ A.
Description or Notation of a Set:-
Usually, sets are represented in the following two ways:
(i) Roster form or Tabular form
(ii) Set Builder form or Rule Method
, (i) Roster for m : In this form, we list all the members of the set within
braces (curly brackets) and separate these by commas.
For example, the set A of all odd natural numbers less than 10 in the
Roster form is written as:
A = {1, 3, 5, 7, 9}
● In roster form, every element of the set is listed only once.
● The order in which the elements are listed is immaterial. For
example, each of the following sets denotes the same set {1, 2, 3},
{3, 2, 1}, {1, 3, 2}.
(ii) Set - B u ilder For m :- In this form, we write a variable (say x)
representing any member of the set followed by a property satisfied by
each member of the set.
For example, the set A of all prime numbers less than 10 in the set-
builder form is written as,
A = {x | x is a prime number less than 10}
Note:- The symbol '|' stands for the words 'such that'. Sometimes, we use
the symbol ':' in place of the symbol '|'.
Sets of Num ber s:-
1. Natural Numbers (N) :- N = {1, 2, 3,4 ,5 6, 7, …}
2. Integers (Z) :- Z = {…, -3, -2, -1, 0, 1, 2, 3, 4, …}
3. Whole Numbers (W) :- W = {0, 1, 2, 3, 4, 5, 6…}
4. Rational Numbers (Q) :- Q = { 𝑝 𝑞 : p Z, q Z, q ≠ 0}
Beginner level
WHAT are SETS?
A set is a collection of well-defined and well distinguished objects
of our perception or thought.
– Example: A = {1, 2, 3, 4, 5}
What is an ELEMENT of a SET?
The objects in a set are called its elements.
So in case of the above Set A,
The elements would be 1, 2, 3, 4, and 5.
We can say, 1 ∈ A, 2 ∈ A etc.
Usually we denote Sets by capital letters like A, B, C, etc, while their
elements are denoted in small letters like x, y, z etc.
Note:-
If x is an element of A, then we say x belongs to A and we represent
it as x ∈ A.
If x is not an element of A, then we say that x does not belong to A
and we represent it as x ∉ A.
Description or Notation of a Set:-
Usually, sets are represented in the following two ways:
(i) Roster form or Tabular form
(ii) Set Builder form or Rule Method
, (i) Roster for m : In this form, we list all the members of the set within
braces (curly brackets) and separate these by commas.
For example, the set A of all odd natural numbers less than 10 in the
Roster form is written as:
A = {1, 3, 5, 7, 9}
● In roster form, every element of the set is listed only once.
● The order in which the elements are listed is immaterial. For
example, each of the following sets denotes the same set {1, 2, 3},
{3, 2, 1}, {1, 3, 2}.
(ii) Set - B u ilder For m :- In this form, we write a variable (say x)
representing any member of the set followed by a property satisfied by
each member of the set.
For example, the set A of all prime numbers less than 10 in the set-
builder form is written as,
A = {x | x is a prime number less than 10}
Note:- The symbol '|' stands for the words 'such that'. Sometimes, we use
the symbol ':' in place of the symbol '|'.
Sets of Num ber s:-
1. Natural Numbers (N) :- N = {1, 2, 3,4 ,5 6, 7, …}
2. Integers (Z) :- Z = {…, -3, -2, -1, 0, 1, 2, 3, 4, …}
3. Whole Numbers (W) :- W = {0, 1, 2, 3, 4, 5, 6…}
4. Rational Numbers (Q) :- Q = { 𝑝 𝑞 : p Z, q Z, q ≠ 0}
