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I have two polygon layers: one indicating countries, and other on top indicating lakes. I want to create a new layer that keeps the countries but have the lakes cut out of them. What tool do I use?

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I think the erase function would more appropriate. Using the symmetrical difference tool if there were any portion of the lake polygons outside of the country polygon they would be added to the output. See the difference in outputs:

(symettrical difference on top, erase on bottom)

enter image description here

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You would use the difference tool to find the area in the Country layer(input layer) that does not appear in the Lake layer(difference layer). In ArcGIS the exact tool name is Symmetrical Difference. A summary of the tool can be found at http://pro.arcgis.com/en/pro-app/tool-reference/analysis/symmetrical-difference.htm.

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