你们在哪里认识的?
Nǐmen zài nǎlǐ rènshi de?
Where did you meet?
What does the character 的 mean in this sentence?
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Nǐmen zài nǎlǐ rènshi de?
Where did you meet?
What does the character 的 mean in this sentence?
This can be seen as an ellipsis of the structure "是...的" which indicates a judgment of something has already happened.
For example:
"我们(we)是[在中国认识](met in China)的"
"他们(they)是[昨天来](came yesterday)的"
One of the functions of 的 is being an adjectival marker that marks a phrase as an adjectival phrase
我们在中国认识 = We met in China
的 marks 在中国认识 as an adjectival phrase that describes 我們
[我們 (topic)] + [在中国认识的 (comment)] = [We] (are someones) [met in China]
你们在哪里认识的? just replaced 中国 with 哪里. 在哪里认识的 is still an adjectival phrase in an Interrogative sentence
Q: 你们(是)在哪里认识的?
A: 我们(是)在中国认识的
In this kind of construction, when 是 X 的 is used, it is not just about the validation of X, but also about the possibility of "other than X" (which is discarded by virtue of the validation of X).
It is more obvious in the following examples when an adjective is used:
It is a known fact that, in Chinese, adjectives associable to degrees of intensity must be used with an adverb of degree in an example like (3). Usually, the adverb 很 is used by default. It does not really mean "very" in this case, but just to indicate that we have a positive value of 珍贵.
In (4), it is not necessary to use an adverb of degree to tilt the balance towards positive. By bringing up the possibility of non-X (i.e. other than X) and then discarding it, 是 X 的 serves to reinforce/confirm/stress the status of positive value of X.