math set theory element complement

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 ..

Difference of two sets A and B, A - B is a set whose elements belong to A but not to B. A - B is called the relative complement of B w.r.t. ..

>- The difference of two sets A and B, in this order, is the set of all those elements of A which are not in B. - The symmetric difference of two sets A and B is defined as the union of the sets A - B and B - A. Important results If A is a subset of..

The Operations on Sets are: Union of sets, Intersection of sets, Disjoint sets, Difference of two sets (Relative complement), Symmetric Difference of two sets, Complement of a set..

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

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..

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, . ..

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

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..

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