The union of a collection of sets is defined as the set of all distinct elements that are in the collection. This includes the specific case where the collection consists of two sets.
That is called the UNION of the two sets.
The union of sets A and B, that is, the set of all elements that are either in A or B (or both).
The union of two sets A and B is a set that consists of all elements which are either in A, or in B or in both.
The set of elements that are elements of the two (or more) given sets is called the intersection of the sets.
That's not true. All sets have zero or more elements. You can have a set with zero elements - the "empty set".
Basically two ways: either by listing all the elements, or by specifying some rule for elements to be included. Listing all the elements only makes sense for finite sets.
A set is a collection of well defined objects known as elements Opperatons of sets are 1)union - the union of sets A and B is the set that contains all elements in A and all elements in B. intersection - given two sets A and B, the intersection of A and B is a set that contains all elements in common between A and B. compliments - given set A, A compliment is the set of all elements in the universal set but not in A difference - A-B is a set containing all elements in A that are not in B. symmetric difference - it is the sum of A and B minus A intersection B.
The union of two sets, X and Y, is the set containing all the elements that are either in X or in Y or in both. Duplicate entries are usually removed.
For example, if you take the set A = {1, 2}, then the following sets are all subsets of it: {}, {1}, {2}, {1, 2}. That is, all the sets that fulfill the condition that all of its elements are also elements of the set "A".
Allowing sets with zero elements simplifies things, in the sense of not requiring all sorts of special cases. For example: the intersection of two sets is another set (which contains all items that are elements of BOTH original sets). Period! If you allow the empty set, there is no need to alter the definition of an intersection, to consider the special case that the sets have no elements in common.
You can specify a set either by listing all of its members (not an option for sets that are very large or even infinite), or by specifying some rule for elements to be a part of the set.
There are various types of sets based on the relationship between their elements. Some common types include: Empty set: A set containing no elements. Singleton set: A set with only one element. Finite set: A set with a countable number of elements. Infinite set: A set with an uncountable number of elements. Subset: A set where all elements are also elements of another set. Proper subset: A subset that is not equal to the original set. Universal set: A set that contains all elements under consideration. Disjoint set: Sets that have no common elements. Power set: A set consisting of all possible subsets of a given set.