# Symmetrical difference

In GIS, symmetrical difference is an analytical process in which two layers are used to create one new layer with the overlapped areas of the original layers. Simply, this analysis process creates a new layer with the features of either one of the original layers, but the new layer does not include the areas where both of the layers existed. The symmetrical difference operation performs the opposite task of the intersect tool, and must use two polygon features in its analysis.[1]

Example of Symmetric Difference overlay. source: CERT Software Engineering Inst.[2]

## Common Applications

Symmetric difference is also used in other fields. In mathematics, the symmetric difference is the set of two or more elements which do not intersect with each other[3]. In a Venn Diagram, the symmetric difference is the union of two parts excluding the intersection. Symmetric difference is represented by ‘XOR’ in Boolean logic [4]

## References

1. ArcGIS Help 10: Symmetrical Difference (Analysis). ESRI. Accessed 5 September 2012.
2. Symmetric Difference. Wikipedia. Accessed 5 September 2012.
3. Weisstein, Eric W. "Symmetric Difference." From MathWorld - A Wolfram Web Resource. Symmetric Difference