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Sitzen vs. setzen

The German verbs sitzen and setzen both relate to sitting, but they are not interchangeable. The key difference lies in state versus action: sitzen describes the state of being seated, while setzen describes the action of putting something or oneself into a seated position.

Sitzen

A1
This verb means to sit or to be seated. It is a stative verb that describes a static condition or position. It answers the question Wo? (Where?).
Die Katze sitzt auf dem Sofa.
(The cat is sitting on the sofa.)
Wir sitzen im Kino in der ersten Reihe.
(We are sitting in the front row at the cinema.)
Der Fleck sitzt tief im Stoff.
(The stain is deep in the fabric.)
Warum sitzt du auf dem Boden?
(Why are you sitting on the floor?)
Meine Brille sitzt schief auf der Nase.
(My glasses are sitting crookedly on my nose.)
Er hat den ganzen Tag am Schreibtisch gesessen.
(He sat at the desk all day.)

Setzen

A1
This verb means to set, to place, or to put. When used reflexively (sich setzen), it means to sit down. It is an active verb that describes a movement or action. It answers the question Wohin? (Where to?).
Ich setze mich auf das Sofa.
(I am sitting down on the sofa.)
Sie setzt das Kind auf den Stuhl.
(She is putting the child on the chair.)
Bitte setzen Sie sich.
(Please have a seat / sit down.)
Er setzt den Koffer auf den Boden.
(He is putting the suitcase on the floor.)
Wohin sollen wir uns setzen?
(Where should we sit down?)
Der Autor hat ein Komma an die falsche Stelle gesetzt.
(The author put a comma in the wrong place.)

Summary

In essence, sitzen is about the state of being in a location (Where? / Wo?), while setzen is about the action of moving to a location (Where to? / Wohin?). If there is movement involved in getting into a seated position, use setzen. If you are already in that position, use sitzen.