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.
3. DIFFERENCE
The difference of sets A and B is the set of elements which belong to A but which do not belong to B. We denote the difference of A and B by A – B
Which is read “A difference B” or, simply, “A minus B”.
Example 3.1: In the Venn diagram in Fig 2.3, we have shaded A – B, the area
in A which is n
A – B is shaded
Fig 2.3
Example 3.2: Let R be the set of real numbers and let Q be the set of rational numbers. Then R – Q consists of the irrational numbers.
The difference of A and B may also be defined concisely by
A – B = {xx∈A, x∉B}
Remark 2.6: Set A contains A – B as a subset, i.e.,
(A – B)⊂A
Remark 2.7: The sets (A – B), A∩B and (B – A) are mutually disjoint, that is, the intersection of any two is the null set.
The difference of A and B is sometimes denoted by A/B or A ~ B