## 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 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 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 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 |

Ã˜ |
Empty set |

P (C) |
Power set |

= |
Equal Set |

Ac |
Complement |

∈ |
Element of |

∉ |
Not an element of |