elements of number theory

: Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B. Cardinality of a Set A: The number of elements in a finite set ..

Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = ..

The total number of all possible subsets of a given set containing n elements is 2 ..

A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite s..

A scalar matrix is a diagonal matrix in which all the diagonal elements are equa..

In roster method of representing a set, all the elements are listed in the set. Two sets are said to be Equivalent sets if the elements of one set can be put in one-one correspondence with the elements of the other set. Two sets are said to be Equal s..

This method is also known as Property method. In this method, a set is represented by stating all the properties which are satisfied by the elements of the set and not by any other element. If A contains all values of 'x' for which the condition P(x) is true, then we write A = ..

Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add the..

A set can be formed by using all the common elements of two given sets. Such a collection is called the intersection of the given set..

Matrices : A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Determinants : ..