SET OPERATIONS

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 = {xx∈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