LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

TYPES OF SET

__TYPES OF SET __

**Finite
set-**

**If the number of elements of a set is finite, the set is
called a finite set**

**Example – a) { The set
of all the month of the year } **

** b) X = { x : x is a factor of 6 }**

** c) The set of even numbers
between 5 to 25 **

** **

**Infinite
Set –**

**If in a set there are don’t have any fixed number of elements
is called an infinite set, such a set has an uncountable number of elements.**

**Example-**

** a) The of all positive
even integers **

** b) The set of integers I = { ………, -8, -7, -6,
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,………….. }**

** c) The set of natural numbers that are greater than 9 = { x :
x ∈ N and x > 9 }**

** **

**Empty
Set –**

**If any A set that does not contain any elements is to be considered as an Empty set, such
a set is donated by { } or φ. An empty set is also called Null Set or a Vold
set,**

**Example –**

** a) the set of women who are 6 meters tall **

** b) the set of odd integers with 6 as a factor**

** c) the set of even prime numbers that are greater than 7**

**the number of elements in an empty set is 0, but { 0 } is not
an empty set because it contains the elements 0.**

**Universal Set –**

**The set of all the
possible objects (or elements), under consideration for a particular discussion, is called the Universal set and it is denoted by U, the universal set may be
different for different problems. **

**Example- **

** Let, A =
{ students of your class who play cricket }**

** B = { students of your class who play football }**

**If our study is regarding the sets A & B, we may take the
set of all the students of your class as the universal set, we may also take
the set of all the students of your school as the universal set, however in a
particular problem there will be only one universal set.**

**Equivalent set –**

**This is to be remembered that, two finite set would be called Equivalent set, whether they contain the
same number of elements, In other words, sets A & B are equivalent sets if
n(A) = n(B), we express this in symbols as A ↔ B**

**Example-**

**The sets A = { 2, 5, 8, 12 }, and B = { 4, 6, 9, 11 } are considered as equivalent sets
because it has been observed that, n(A) = n(B) = 4, In symbol A ↔ B.**

**Singleton Set –**

**A set that has only
one element is called a Singleton Set.**

**
**

**Example – Each of the sets { 0 }, { 2 }, { 5 } are Singleton set.**