inverse conclusion
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conversely
A conclusion drawn from the fact that a certain statement was not made or that the opposite of a condition applies. It means something like 'from this, the reverse follows.'
Er hat nur die guten Seiten erwähnt; im Umkehrschluss bedeutet das wohl, dass es auch Nachteile gibt.
He only mentioned the good sides; conversely, that probably means there are disadvantages too.
'Umkehrschluss' (inverse conclusion) consists of 'die Umkehr' (the reversal, the opposite) and 'der Schluss' (the conclusion). So it is literally a conclusion that you draw from the opposite of a statement.
Wenn das Licht aus ist, ziehe ich den Umkehrschluss, dass niemand zu Hause ist.
If the light is off, I draw the inverse conclusion that no one is at home.
This noun is used almost exclusively in the fixed expression 'im Umkehrschluss' (conversely/by inverse conclusion). It introduces a sentence or subordinate clause that expresses a logical conclusion.
Das Restaurant hat heute geschlossen. Im Umkehrschluss müssen wir uns etwas anderes zum Abendessen suchen.
The restaurant is closed today. Conversely, we have to look for something else for dinner.
When the expression 'im Umkehrschluss' (conversely) is at the beginning of the sentence (position 1), the conjugated verb follows directly in position 2. This word order is called inversion.
Sie hat nicht widersprochen. Im Umkehrschluss stimmte sie dem Plan also zu.
She did not object. Conversely, she therefore agreed to the plan.
conclusion
'Schlussfolgerung' and 'Umkehrschluss' both have to do with logical thinking. A 'Schlussfolgerung' is generally a result that you derive from facts or observations. An 'Umkehrschluss' is more specific: you mentally reverse a statement and say what follows from it in the opposite direction. This is not always automatically correct, so 'im Umkehrschluss' often sounds somewhat cautious or argumentative. For a normal logical result, use 'Schlussfolgerung'. If this reversed way of thinking is explicitly meant, 'Umkehrschluss' fits.
Wenn nur Mitglieder Rabatt bekommen, heißt das im Umkehrschluss, dass Gäste den vollen Preis zahlen.
If only members get a discount, then conversely, guests pay the full price.
Nach dem Test war unsere Schlussfolgerung, dass die neue App noch zu langsam ist.
After the test, our conclusion was that the new app is still too slow.