specified / predetermined
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specified
Set, determined, or established as a condition in advance. Something is not freely selectable, but already defined.
Die Teilnehmer müssen den Aufsatz über ein vorgegebenes Thema schreiben.
The participants must write the essay on a specified topic.
'Vorgegeben' (specified/predetermined) is the past participle of the separable verb 'vorgeben' (to specify/set in advance). The prefix 'vor-' means 'in advance,' so something is 'vorgegeben' when it has been 'given' or set in advance.
Der Lehrer gibt die Themen für die Präsentationen vor.
The teacher specifies the topics for the presentations.
This adjective is often combined with nouns that describe a framework or structure. Typical examples are: 'ein vorgegebener Zeitplan' (a specified schedule), 'eine vorgegebene Struktur' (a specified structure), 'ein vorgegebener Rahmen' (a specified framework), or 'ein vorgegebener Betrag' (a specified amount).
Bitte halten Sie sich an die vorgegebene Struktur für den Bericht.
Please stick to the specified structure for the report.
The word emphasizes that there is no free choice, or only very limited free choice. If something is 'vorgegeben' (specified), you have to follow this rule, condition, or information.
Die Regeln des Spiels sind klar vorgegeben und können nicht geändert werden.
The rules of the game are clearly specified and cannot be changed.
certain / specific
'bestimmt' and 'vorgegeben' can both mean that something is not free or arbitrary. 'bestimmt' often describes something specific or something intended for a purpose. 'vorgegeben' emphasizes more strongly that someone else has already set something in advance and that you have to follow it. The word fits well with rules, tasks, times, or conditions. Learners may confuse the words because both express a clear choice. Remember: 'bestimmt' can simply mean 'specific'; 'vorgegeben' usually means 'set in advance and not freely selectable'.
Bei der Prüfung ist die Zeit für jede Aufgabe vorgegeben.
In the exam, the time for each task is specified.
Nach dem Gespräch sucht er nach einem bestimmten Buch für den Kurs.
After the conversation, he looks for a specific book for the course.