math set theory element

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 number of elements in a finite set A, is the cardinality of A and is denoted by n(A..

If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..

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 sets..

Union of sets - If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..

Capital letters are usually used to denote or represent a set. viz., A, B, C, D, . . . . The elements of sets are usually represented by lower case letters. viz., a, b, c, x, y, . ..

Summary - A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the pr..

The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S). If a set S is finite, say S has n elements, then the power set of S can be shown to have 2 n elements..

Let U be a universal set, A be any subset of U, then the elements of U which are not in A i.e., U - A is the complement of A w.r.t. U is written as A' = U - A = A c ..

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