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I have two sets of polygons in shapefiles. One set of polygons is composed of a full and exclusive set of smaller polygons. But the smaller polygons are not tagged as which larger polygon they were used to build. Is there a way in QGIS to determine which smaller polygons make up the larger polygons and tag the smaller polygons with the ID of the larger polygon that is belongs to?

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I found the correct command in QGIS. Vector-->Geoprocessing Tools-->Intersection. Set the larger polygons as the Input Layer and the smaller polygons as the Output Layer.

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