Available with Spatial Analyst license.
Summary
Performs a Combinatorial Or operation on the cell values of two input rasters.
If either input value is true (non-zero), the output is a different value for each unique combination of input values. If both inputs are false (zero), the output value is 0.
Illustration

Usage
- The Combinatorial math tools interpret the inputs as Boolean values, where nonzero values are considered true, and zero values are considered false. 
- Two inputs are necessary for this Combinatorial evaluation to take place. 
- The order of inputs for this tool is only relevant for the output attribute table. 
- See Analysis environments and Spatial Analyst for additional details on the geoprocessing environments that apply to this tool. 
Syntax
CombinatorialOr (in_raster_or_constant1, in_raster_or_constant2)
| Parameter | Explanation | Data Type | 
| in_raster_or_constant1 | The first input to use in this combinatorial operation. It must be of positive integer type. A number can be used as an input for this parameter, provided a raster is specified for the other parameter. To be able to specify a number for both inputs, the cell size and extent must first be set in the environment. | Raster Layer | Constant | 
| in_raster_or_constant2 | The second input to use in this combinatorial operation. It must be of positive integer type. A number can be used as an input for this parameter, provided a raster is specified for the other parameter. To be able to specify a number for both inputs, the cell size and extent must first be set in the environment. | Raster Layer | Constant | 
Return Value
| Name | Explanation | Data Type | 
| out_raster | The output raster. The output is always of integer type. | Raster | 
Code sample
CombinatorialOr example 1 (Python window)
This example performs a Combinatorial Or operation on two GRID rasters and outputs the result as an IMG raster.
import arcpy
from arcpy import env
from arcpy.sa import *
env.workspace = "C:/sapyexamples/data"
outCOr = CombinatorialOr("degs", "cost")
outCOr.save("C:/sapyexamples/output/outcor.img")
CombinatorialOr example 2 (stand-alone script)
This example performs a Combinatorial Or operation on two GRID rasters.
# Name: CombinatorialOr_Ex_02.py
# Description: Performs a Combinatorial Or operation on the cell
#              values of two input rasters
# Requirements: Spatial Analyst Extension
# Import system modules
import arcpy
from arcpy import env
from arcpy.sa import *
# Set environment settings
env.workspace = "C:/sapyexamples/data"
# Set local variables
inRaster1 = "degs"
inRaster2 = "cost"
# Check out the ArcGIS Spatial Analyst extension license
arcpy.CheckOutExtension("Spatial")
# Execute CombinatorialOr
outCOr = CombinatorialOr(inRaster1, inRaster2)
# Save the output 
outCOr.save("C:/sapyexamples/output/outcor")
Environments
Licensing information
- ArcGIS Desktop Basic: Requires Spatial Analyst
- ArcGIS Desktop Standard: Requires Spatial Analyst
- ArcGIS Desktop Advanced: Requires Spatial Analyst