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I have got a number of polygons within a single larger polygon. Parts of the smaller polygons go out from under the larger one, and I want to delete the parts of the smaller polygons, that go outside the larger one. How can this be done?

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    Welcome to Geographic Information Systems! Welcome to GIS SE! We're a little different from other sites; this isn't a discussion forum but a Q&A site. Your questions should as much as possible describe not just what you want to do, but precisely what you have tried and where you are stuck trying that. Please check out our short tour for more about how the site works. – Ian Turton Sep 10 '20 at 12:51
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If your dataset is simple enough - one large polygon, you could use the clip function (menu Vector>Geoprocessing>Clip). First select the large polygon and export it into a new layer and use that as the overlay layer.
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You want to clip (QGIS -> Vector -> Geoprocessing Tool -> Clip) your smaller polygons with your larger polygon. This tutorial describes how to do this.

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