Set Theory Index

Relations.

Relations.

What is Relation? Any subset of a Cartesian product A×B  in which the first element and second element of ordered pairs have special relation to each other is known as “Relation”. A relation from one  set (A)  to another set (B) is denoted by: “xRy” or simply “R” Where (x,y)∈R For example: If set A={Me , My father , My son} And set B={My spouse , My mother , My daughter} Then one of the “Relation” from set A to set B can be: R=[{My spouse , Me} , {My mother , My father}] In above...

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Cartesian product of two sets.

Cartesian Product: The Cartesian Product of two sets A and B is the set of all Ordered Pairs (a,b)  where the first element of order pairs “a” belongs to first set “A” and second element of ordered pairs “b” belongs or second set “B”. Or a∈A and b∈B Note: Cartesian product of set A and B is not equal to Cartesian product   of set B and A. Denotation of Cartesian product: Cartesian product of sets “A” and “B” is denoted by : A×B And Cartesian product of...

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Ordered pairs.

Prior to understanding what is ordered pair let us know what is a pair first. What is a pair? A pair is a set  which have only two elements. Like {a,b} , {me,my sister}. A pair can never have more than or less than two elements ; it always have exactly two elements. What is ordered pair? A pair or set of two elements , in which order of its elements are predefined or the first element is always in first and second is always in second is known as an ordered pair. An ordered pair having “a is its first element and “b” as its...

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Real Number System.

Real Number System.

Prior to understand “Real Numbers” we need to understand the concept of Number system. So , What is Number? Number is one of the basic concept of mathematics. A Number basically representation of quantity of any object. Number system started from the time of ancient civilization , Primitive man used to compare one quantity with another when there was no number ; Like they used to lay aside each pebble for a sheep they rear , in order to count sheep.  latter with advancement in language they gave the number a name and a symbol...

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Set Operations.

Set Operations.

The Process of making a new sets from two or more given sets applying some special rules is known as set operations. If we are given two sets , then there are three standard ways to construct new sets from them. The three operations are called binary set operations , which are as following: Union: A set that contains all the elements contained by first set (A) and second set (B) is known as union of the two sets (A and B). We denote union of two sets (A and B) by symbol A ∪ B. For example: if A={1,2,3} and B={3,4,5} Then, A ∪...

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Venn diagram

Venn diagram

Venn diagram is a graphical representation of sets and relation between sets. Venn diagram is the diagram which shows the possible relations between the finite collections of set. Venn diagram was introduced in 1880 by john Venn. It is constructed by more than two circles which is generally overlapping . To draw the Venn diagram, you first draw the rectangular which is called “universe” then you draw the required quantity of circle for the collection of set. Whole elements of the set are inside the universe. The elements which are in...

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Relation between sets.

If , in any condition two or more sets appears in discussion they might have some special relation between each other. There are many types or relation that might occur between two or more sets. Those relations are: Subset: If one set (A) contains  all the elements that another set (B) contains then the second set (B) is called to be the subset of first set (A) , or set B contains set A. In symbol we write A ⊂ B  (A is contained in B) , B ⊃ A (B contains A) Both symbols above means that set A is a subset of set B. A set may have two...

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Introduction to Set Theory

Introduction to Set Theory

Introduction to Set Theory: The concept of modern mathematics is started with set. Set appears in all branches of mathematics. The main developer of set theory is George Cantor (1845-1915 AD). The word set is synonym with “Collection” , “Class” or “Aggregate”. Basically set is a collection or organization of similar objects (an object may be material or conceptual). and the objects by which a set is made of  are called elements or member of the set. Some example of set are: 1> The countries of...

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