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Equal Sets
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 = ..
or
A set A is said to be a proper subset of B if B contains at least one element, which is not in..
Total number of subsets in a set is 2n
The total number of all possible subsets of a given set containing n elements is 2 ..
(i) Roster Method
This method is also known as tabular method. In this method, a set is represented by listing all the elements of the set, the elements being separated by commas and are enclosed within flower brackets {..
Finite and Infinite Sets
A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite s..
Cardinality of a Set A
The number of elements in a finite set A, is the cardinality of A and is denoted by n(A..
Scalar Matrix
A scalar matrix is a diagonal matrix in which all the diagonal elements are equa..
Singleton Set or Singlets
A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is ..
Summary
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..
Determinants
Let A = [aij] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the squ..
Result
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