In the given text, you are asked to identify the propositions and specify their nature.
1. Je n'arrive pas à travailler : il fait trop chaud.
In this sentence, the proposition is "Je n'arrive pas à travailler" (I can't work), and its nature is a main (independent) clause. The reason given for not being able to work is "il fait trop chaud" (it's too hot), which is another independent clause. Both clauses can stand alone as complete sentences.
2. Sors,/cours/et rapporte le goûter.
Here, the proposition is "Sors, cours, et rapporte le goûter" (Go out, run, and bring back the snack). This is an imperative sentence giving commands, where the subject "tu" (you) is implied. The nature of this proposition is a command or imperative sentence.
3. Les amis dont je t'ai parlé arriveront ce soir.
The proposition here is "Les amis dont je t'ai parlé arriveront ce soir" (The friends I told you about will arrive tonight). This is a complex sentence with a main (independent) clause "Les amis dont je t'ai parlé arriveront ce soir" and a relative clause "dont je t'ai parlé" (whom I told you about). The nature of the main clause is independent, while the relative clause adds additional information about the friends.
Lastly, the provided text "La nuit était déjà tombée lorsque j'entendis que des pas se rapprochaient de la maison" seems to be incomplete or not directly related to the question of identifying propositions and their nature. If you need assistance with this text or have any other questions, feel free to ask!
