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...
read moreReal 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...
read moreSet 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 ∪...
read moreVenn 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...
read moreRelation 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...
read moreIntroduction 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...
read moreThe Cosine Law
Statement of cosine law: Cosine Law states that in any triangle following equations can be implied: Where “a” is the side opposite to vertex A , ”b” is the side opposite to vertex B and “c” is the side oposite to vertex C , or ”a” , “b” , “c” are the three sides of a triangle and “A” , “B” , “C” are three angles of the triangle. Derivation of Cosine Law: We can prove the above stated equations by following way: To prove the first of...
read moreTypes of matrices
Matrix theory is one of most important topic in mathematics , so it must be studied in detail to solve the mathematical problems with the help of matrix. One of the step in studying matrix is to study it’s types and example. Different types of matrices and it’s details are described below: Note that it is possible for some matrices to belong in more than one type. Types of matrices are as follows: 1> Row matrix: A matrix having only one row is known as row matrix. for example: , , 2>Column matrix: A matrix , having only...
read moreWhat is matrix
The theory of matrix is a powerful tool in modern mathematics. It is especially useful in the system of linear equations, linear transformation and many other filed of physics, chemistry, engineering and social science. What is matrix?: Matrix is a rectangular array of numbers arranged in row (horizontal lines) and columns (vertical lines) usually a matrix is enclosed between round or square brackets. Example: 1> 2> Usually matrix are denoted by a capital letter and two subscription. Example: Where “i” denotes the number of rows...
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