thus
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thus
Introduces a logical result or consequence of something previously mentioned; therefore, consequently.
Der Hauptredner ist krank geworden, somit muss die Veranstaltung leider ausfallen.
The keynote speaker has fallen ill; thus, the event unfortunately has to be canceled.
When 'somit' (thus) stands at the beginning of a sentence, the conjugated verb moves to second position. It can also stand after the verb to emphasize the consequence less strongly.
Der Zug hatte Verspätung, somit verpasste ich meinen Anschluss.
The train was delayed; thus, I missed my connection.
'Somit' (thus) is often used in written language or in formal contexts to make a logical conclusion clear and explicit. It often sounds more objective and formal.
Die Beweise sind eindeutig, somit ist der Fall abgeschlossen.
The evidence is clear; thus, the case is closed.
The word is made up of 'so' and 'mit'. It literally means 'with that' or 'in this way' and introduces a direct consequence of what was said before.
Alle Flüge wurden gestrichen, somit mussten wir im Hotel übernachten.
All flights were canceled; thus, we had to stay overnight at the hotel.
then
'dann' and 'somit' can both express a result. 'dann' is very general and fits in many everyday situations, including simple conditions: if something happens, something else happens as a result. 'somit' sounds more precise and somewhat more formal. It clearly shows that a logical consequence follows from what was said before. In conversations, people often say 'dann'; in explanations, reports, or summaries, 'somit' is often a better fit.
Der Bus fällt aus, somit kommen viele Mitarbeiter heute später.
The bus is canceled, so many employees will arrive later today.
Wenn ihr früher fertig seid, können wir dann zusammen essen.
If you finish earlier, then we can eat together.