SET OPERATIONS
In arithmetic, we learn to add, subtract and multiply, that is, we assign to each pair of numbers x and y a number x + y called the sum of x and y, a number x – y called the difference of x and y, and a number xy called the product of x and y.
These assignments are called the operations of addition, subtraction and multiplication of numbers. In this unit, we define the operation Union, Intersection and difference of sets, that is, we will assign new pairs of sets A and B. In a later unit, we will see that these set operations behave in a manner some what similar to the above operations on numbers.
6. SUMMARY
The basic set operations are Union, Intersection, Difference and Complement
defined as:
The Union of sets A and B, denoted by A∪B, is the set of all elements, which belong to A or to B or to both.
The intersection of sets A and B, denoted by A∩B, is the set of
elements, which are common to A and B. If A and B are disjoint then their intersection is the Null set ∅
The difference of sets A and B, denoted by A – B, is the set of elements which belong to A but which do not belong to B.
The complement of a set A, denoted by A’, is the set of elements, which do not belong to A, that is, the difference of the universal set U and A.