Union and Intersection

Sets are a well-defined group of data/objects that may be found in a database. The data/objects are all members of the same group, yet each data is distinct from the others. As an example, if the word “application” is required to be placed in a Set, it will look something like this: Set A={a, p, l, I c, t, o, n}, where the letters that are repeated throughout the word, such as “p,” “a,” and I are only written once because they are the same elements that are repeated multiple times.

Definition of union and intersection

A Set’s Union

A set’s union is defined as the set that contains all of the elements from both sets A and B. The phrase “OR” is used to denote a set’s union, which signifies that if data exists in either A or B, it will be included in the set’s union. “∪” is the sign for the union of a set. If x A B, then x A or x B can be stated as the conventional definition.

A Set’s Intersection

A set’s intersection is defined as the set that contains all of the items from both sets A and B. The intersection of the sets is represented by the word “AND,” which implies that the components in the intersection are present in both A and B. The symbol “∩” is used to represent the set’s Intersection. If x A B, then x A and x B can be stated as a standard definition.

Examples of union and intersection

The set that contains all the items that are common to both sets is called the intersection of sets for two given sets. “∩” is the symbol denoting the intersection of sets. The intersection, A B (read as A intersection B) shows all the items that are present in both sets and are the common elements of A and B for any two sets A and B.

Set A = {1,2,3,4,5}, and Set B ={ 3,4,6,8}, for example, A B = {3,4}.

Intersection and Union

The set of items that belong to either A or B, or perhaps both, is defined as the union of two sets A and B. It is simply defined as the collection of all distinct elements or members that belong to any of these sets. The union operator is represented by the symbol and corresponds to the logical OR. It is the smallest set that contains all of the elements from both sets. If set A is 1, 2, 3, 4, 5, and set B is 3, 4, 6, 7, 9, then the union of A and B is represented by AB and expressed as 1, 2, 3, 4, 5, 6, 7, 9. There is no need to include the numbers 3 and 4 twice because they appear in both sets A and B. Because few integers are shared by both sets, the number of items in the union of A and B is clearly less than the total of the separate sets.

The set of elements that belong to both A and B is defined as the intersection of two sets A and B. It is simply defined as the set comprising all members of set A that also belong to set B, and all elements of set B that also belong to set A. The intersection operator is denoted by the symbol and corresponds to the logical AND. The intersection of two sets, on the other hand, is the biggest set that contains all of the items shared by both sets. For instance, if set A is 1, 2, 3, 4, 5, and set B is 3, 4, 6, 7, 9, the intersection of A and B is represented by AB and expressed as 3, 4. Because only the numbers 3 and 4 are shared by both sets A and B, they are referred to as the sets’ intersection.

Conclusion

Sets can be joined and connected using union and intersection procedures. In set theory, union is the set of all items in both sets, whereas intersection is the set of all distinct elements in both sets. The intersection of two sets A and B is denoted as“A∪B A set is a collection of well-defined things, such as numbers and functions, referred to as elements.