Пусть он поспит на диване.

Questions & Answers about Пусть он поспит на диване.

How does the prefix по- change the meaning of the verb here?
The prefix по- adds the meaning of doing an action for a short, limited amount of time. While спать just means "to sleep," the perfective verb поспать means "to sleep for a bit" or "to take a nap." Here, поспит suggests letting him rest for a little while rather than for a full night.
Why is поспит conjugated in the future tense if the English translation is a command ("Let him sleep")?
The word пусть is a particle used to create third-person commands or wishes ("let him", "let them"). In Russian, this structure uses пусть plus the present or future tense of the verb. Because поспать is a perfective verb, its conjugated form поспит is technically in the future tense, but combined with пусть, it forms a present-moment command.
Could I use давай instead of пусть to say "let" in this sentence?
No, they have different jobs. Давай (or давайте) is used for "let's" when you are suggesting an action that includes yourself (e.g., "Let's sleep"). Пусть is used when you are talking about a third party ("Let him/her/them sleep").
Why is диване in the prepositional case here?
Because it indicates the static location where the sleeping is happening, answering the question "where?". When paired with the preposition на (on), the masculine noun диван (couch/sofa) takes the prepositional ending to become на диване.

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