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Differences in Set Theory

In mathematics, a set is an unordered group of objects with no duplicates. The objects in the set can themselves be sets. Two sets are equivalent if they have exactly the same objects in them. Two sets are "disjoint" if they have no objects in common. Since the basis for set theory is boolean (true or false), i.e. an object is either a member of a set or not, a set is either equal to another set or not. Set theory is complementary to Boolean algebra, which is frequently used in computer science. It is possible to do various mathematical operations on sets, one of which is the differences.
  1. Set Union

    • The union of two sets, A and B, is also a set. This union set contains all the elements in both A and B. So the union is the sum of set A and set B. The union is usually written with a symbol that looks like a U. If you have a set of two apples, and a set of two pears, the union of these two sets will contain four fruits: Two apples and two pears.

    Set Intersection

    • Another set operation is the intersection. An intersection of two sets contains only elements which are present both in set A and set B. If we have two sets, one with two oranges and two apples, and another set with the same two apples and two pears, the intersection is the apples. Intersection is usually written with a symbol that looks like an inverted U.

    Set Complimentarity

    • The compliment in set theory means everything except those objects in the set. In set theory, there is a term called "universal set" which basically means "everything." So the complement of set A is all of the objects in the universal set except those in set A. To use fruit again, if you have four apples, the complement of those four apples is all other apples in the universe.

    Set Difference

    • In set theory, the difference between sets A and B is another set. It contains all elements of A that are not elements of B. In the example where A is two apples and two pears, and B is two pears, the difference is two apples.


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