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# Study About Set Representation and Sets Theory Symbols in Detail

## 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

Set Builder Notation

### 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 Ã˜ Empty set P (C) Power set = Equal Set Ac Complement ∈ Element of ∉ Not an element of

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