1. Paris is the capital of France.

2. Paris is a capital of France.
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Sentence 1 is right. Sentence 2 is wrong. By the way, why do we have to use 'the' before 'capital'? Is that because 'the capital of France ' is the only one in the world of in France?

Yes. There is only one capital in a country, therefore the use of "the." The use of "a" implies there's more than one!

Yes, you are correct. In the first sentence, "the" is used before "capital" to indicate that Paris is the specific capital of France. This usage suggests that there is only one capital city in France. Adding "the" distinguishes Paris as the unique capital among all other cities in France.

In the second sentence, the absence of "the" makes it incorrect. Without "the," the sentence implies that Paris is just one of the capital cities in France, rather than being the specific capital city.

To summarize, "the" is used before "capital" to specify that the city being referred to is the only capital in a particular country or region. Its usage indicates a definite and specific nature.