legitim
legitimate
Legally recognized or lawful; in accordance with the law.
Der gewählte Präsident ist der legitime Vertreter des Volkes.
The elected president is the legitimate representative of the people.

legitimate
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legitimate
Legally recognized or lawful; in accordance with the law.
Der gewählte Präsident ist der legitime Vertreter des Volkes.
The elected president is the legitimate representative of the people.

The word 'legitim' (legitimate) comes from the Latin word for law ('lex'). This origin helps you understand and remember the basic meaning of 'lawful' or 'legal'.
Die Opposition zweifelt an der Legitimität der Wahl.
The opposition doubts the legitimacy of the election.
In the meaning of 'lawful', 'legitim' (legitimate) is often used in political or legal contexts. Typical combinations are 'legitimer Nachfolger' (legitimate successor), 'legitime Regierung' (legitimate government), or 'legitimer Erbe' (legitimate heir).
Nach dem Tod des Königs gab es Streit um den legitimen Thronfolger.
After the king's death, there was a dispute over the legitimate heir to the throne.
In the meaning of 'justified', the structure 'Es ist legitim, etwas zu tun' (It is legitimate to do something) is often used. This construction with an infinitive with 'zu' is very common for describing an action as acceptable.
Es ist legitim, mit der Entscheidung nicht einverstanden zu sein.
It is legitimate to disagree with the decision.
This meaning is often recognizable from nouns that express an opinion, a wish, or a demand. Typical combinations are 'eine legitime Frage' (a legitimate question), 'ein legitimes Interesse' (a legitimate interest), or 'ein legitimer Wunsch' (a legitimate wish).
Der Wunsch nach mehr Freizeit ist ein legitimes Anliegen der Mitarbeiter.
The desire for more free time is a legitimate concern of the employees.
understandable
'verständlich' and 'legitim' can both express that a reaction or demand is not simply wrong. 'verständlich' mainly shows that you can relate to the reasons on a human level. 'legitim' sounds more like justified, allowed, or generally acceptable; sometimes it is also about law and rules. That is why 'verständlich' is often suitable for feelings, while 'legitim' fits better when you want to say that a demand or decision is objectively or legally acceptable.

Es ist legitim, dass wir vor der Operation eine zweite Meinung einholen.
It is legitimate for us to get a second opinion before the operation.
Nach dem langen Warten war ihre Ungeduld verständlich.
After the long wait, her impatience was understandable.