Sign In
The symmetric difference of two sets contains the elements which are in either set but not in their intersection. It is denoted by △
and can also be called disjunctive union. In a Venn diagram, the symmetric difference of A and B can be shown as the non-overlapping region of the sets.
There are several ways in which the symmetric difference can be thought of. Two of them are shown in the table.
| A △ B | |
|---|---|
| Words | Symbols |
| The union of the relative complements of A and B. | (A-B) ⋃ (B-A) |
| The difference between the union of A and B and the intersection of A and B. | (A⋃ B)-(A⋂ B) |
Consider an example. U&={1,2,3,4,5,6,7,8,9} A&={1,2,3} B&={3,4,5,6} In this case, the symmetric difference of A and B contains the elements 1,2,4,5, and 6. A △ B = { 1,2,4,5,6 } Note that all the elements of the union of A and B are considered except 3. This is because the number 3 is in the intersection of these two sets. This example can be illustrated with a Venn diagram.
