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Introduction to Set theory

Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set.
Introduction to Set theory

A Set is an unordered collection of objects, known as elements or members of the set.
An element ‘a’ belong to a set A can be written as ‘a ∈ A’,  ‘a ∉ A’ denotes that a is not an element of the set A.

Representation of a set

Three common methods used for representing set:


1. Statement form: In this representation, the well-defined description of the elements of the set is given. Example:

i. The set of all even number less than 10.
ii. The set of the number less than 10 and more than 1


2. Roaster form or tabular form method: In this representation, elements are listed within the pair of brackets {} and are separated by commas.

for example: N={1,2,3,4,5}


3. Set Builder method. In Set-builder set is described by a property that its member must satisfy.

for example: {x : x is natural number less than 10}.

Equal sets
Two sets are said to be equal if both have same elements. For example A = {1, 3, 9, 7} and B = {3, 1, 7, 9} are equal sets.

Subset

A set A is said to be subset of another set B if and only if every element of set A is also a part of other set B.
Denoted by ‘‘.
‘A ⊆ B ‘ denotes A is a subset of B.

https://www.geeksforgeeks.org/wp-content/uploads/gq/2015/06/asubsetB.png

‘U’ denotes the universal set.
Above Venn Diagram shows that A is a subset of B.

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Mathematics | Introduction of Set theory - GeeksforGeeks
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https://www.geeksforgeeks.org/set-theory/

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