Study About Set Representation and Sets Theory Symbols in Detail
Set Theory
is the study of sets and their properties in mathematics. A set is a collection
of items. The objects of a given set are its elements. The study of such sets
and the links that exist between them is known as set theory. Set theory has
shown to be a very helpful tool in defining some of mathematics' most difficult
and important structures. As a result, it is a significant component of the
numerical ability/quantitative aptitude syllabus in a variety of competitive
tests.
On that
note, let’s discuss Set Representation and Set Theory Symbols in detail for in-depth study.
Sets Representation
Sets can be
represented in two ways:
● Roster Form or Tabular form
Roster Form
All of the
elements in the set are listed in roster form, separated by commas and enclosed
by curly braces { }.
In Roster
form, for example, if the set covers all leap years between 1999 and 2017, it would be expressed as
A ={2000,
2004, 2008, 2012, 2016,}
In the
roster form, the order of elements in a set is irrelevant; the order might be
ascending or descending.
Furthermore,
frequency is neglected when representing the sets. For example, if X represents
a set containing all of the letters in the word APPLE, the correct Roster form
representation would be
X ={A, P, L,
E }= {E, L, P, A}
Set Builder Form
In set
builder form, all elements share a property. This property does not apply to
objects that are not members of a set.
For
instance, if set S contains only even prime numbers, it is denoted as
S= { x: x is
an odd natural number}
where x is
an odd natural number
where 'x' is
a graphical representation of the element
':' stands
for 'such that'.
'{}' denotes
'the full set.'
S = x:x is
an even prime number and can thus be interpreted as "the set of all x such
that x is an even prime number." The roster form for this set S is S = 2.
There is only one element in this set. Such sets are referred to as Singleton
Sets.
Common Symbols used in Set Theory
A variety of
symbols are used to represent common sets. Let's go into detail about each of
them.
|
Symbol |
Corresponding set |
|
N |
It denotes the set of all natural numbers, that
is, all positive integers. Examples: 1, 12, 163, 823 and so on. |
|
Z |
It is used to represent the full number set.
This symbol is derived from the Greek word 'Zahl,' which means 'number.' Positive integers are represented by Z+,
whereas negative integers are represented by Z-. Examples: -12, 0, 1237 etc. |
|
Q |
It stands for the collection of rational
numbers. The word "Quotient" is the basis for the sign. As the
quotient of two integers, positive and negative rational numbers are denoted
by Q+ and Q-, respectively (with a non-zero
denominator). Examples: 16/17, -6/7 etc. |
|
R |
It is used to represent real numbers as well as
any other number that may be stated on a number line. Positive and negative real numbers are
represented by R+ and R-, respectively. Examples: 2.67, Ï€, 2√3, etc. |
|
C |
It is used to represent a collection of complex
numbers. Examples: 2+ 5i, i, etc. |
Other
symbols:
|
Symbols |
Symbol Name |
|
{} |
Set |
|
U |
Union |
|
∩ |
Intersection |
|
⊆ |
Subset |
|
⊄ |
Not a subset |
|
⊂ |
Proper subset |
|
⊃ |
Proper superset |
|
⊇ |
Superset |
|
⊅ |
Not superset |
|
Ø |
Empty set |
|
P (C) |
Power set |
|
= |
Equal Set |
|
Ac |
Complement |
|
∈ |
Element of |
|
∉ |
Not an element of |