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 , M
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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.
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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
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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
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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 unio
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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 y
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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 symb
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Introduction:
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
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