Mater rogat utrum convivae lac an vinum recipere velint.

Utrum ... an is the standard Latin way to introduce an either/or indirect question.

So:

• utrum = whether
• an = or

In this sentence, utrum convivae lac an vinum recipere velint means:

whether the guests want to receive milk or wine

A useful pattern to remember is:

• utrum A an B = whether A or B

Because this is an indirect question, and Latin normally puts the verb of an indirect question in the subjunctive.

Here the direct question would be something like:

• Convivae lac an vinum recipere volunt?
  = Do the guests want to receive milk or wine?

But once that question is reported after rogat (asks), Latin changes the verb to the subjunctive:

• Mater rogat utrum ... velint.

So:

• volunt = indicative, used in a direct statement/question
• velint = subjunctive, used in the indirect question

Velint is present subjunctive active, 3rd person plural, from velle (to want).

It is present because the wanting is happening at the same time as the asking. In other words, the mother is asking what the guests want now.

So:

• rogat = she asks
• velint = they may want / they want in an indirect-question construction

In English we usually just say want, but Latin uses the present subjunctive because of the grammar of indirect questions.

Convivae is one of those forms that can look ambiguous, because it could in principle be:

• nominative plural = guests
• genitive singular = of the guest
• dative singular = to/for the guest

But in this sentence it must be nominative plural because it is the subject of velint:

• velint = they want

So the people doing the wanting are convivae = the guests.

A native English speaker often needs to get used to this: in Latin, you often decide the case from the syntax of the whole sentence, not just from the ending by itself.

They are both accusative singular, because they are the objects of recipere.

The guests want to receive what?

• lac = milk
• vinum = wine

So both words function as direct objects.

A useful detail:

• vinum is easy to recognize as accusative singular neuter of a 2nd-declension noun.
• lac may look surprising, but it is a neuter 3rd-declension noun, and neuter nouns have the same form in the nominative and accusative singular.

So lac can mean both milk as subject and milk as object, depending on context.

Because lac, lactis is a neuter noun.

For neuter nouns in Latin:

• nominative singular = accusative singular

So:

• nominative singular: lac
• accusative singular: lac

There is no lactem here. A learner used to masculine/feminine patterns may expect a different accusative form, but neuter nouns often do not change in the singular nominative/accusative.

Literally, recipere means to receive, take, or accept.

In this context, the idea is probably something like:

• to take
• to have
• to accept

So the sentence is asking whether the guests would like milk or wine.

Latin often uses a verb whose basic meaning is a little more literal than the most natural English translation. Depending on context, recipere could be translated in different ways, but here it clearly refers to what drink they want to be given.

Because an is the normal word used in an alternative question after utrum.

So Latin says:

• utrum ... an ... = whether ... or ...

By contrast:

• aut and vel are the ordinary coordinating words for or in statements, not the usual pair for this kind of interrogative structure.

So in a sentence like this, an is exactly what you expect.

Yes. The whole clause beginning with utrum is an indirect question.

Main clause:

• Mater rogat = Mother asks

Indirect question:

• utrum convivae lac an vinum recipere velint
  = whether the guests want to receive milk or wine

This is one of the most important constructions in Latin:

• a verb of asking, knowing, seeing, telling, etc.
• followed by a question word or question structure
• with a subjunctive verb in the subordinate clause

Because rogare can introduce the content of a question.

Here, the sentence focuses on what is being asked, not explicitly whom the mother asks.

So:

• Mater rogat ... = Mother asks ...
• then Latin gives the content of the question: whether the guests want milk or wine

If Latin wanted to make the person asked explicit, it could do so, but it is not necessary here. English also often leaves this unstated: Mother asks whether the guests want milk or wine.

Because it depends on velint.

The structure is:

• velint recipere = want to receive

This is exactly like English:

• they want to receive
• they want to take

So:

• velint = finite verb, they want
• recipere = infinitive, to receive

The direct objects of the infinitive are lac and vinum.

Latin word order is more flexible than English word order, because the endings show the grammatical relationships.

Here we have:

• Mater = subject of the main verb
• rogat = main verb
• utrum ... velint = indirect question
• convivae = subject of velint
• lac an vinum = the alternatives
• recipere = infinitive depending on velint

A very literal layout is:

Mother asks whether the guests milk or wine to receive want.

That sounds unnatural in English, but it is normal in Latin for the important verb of a subordinate clause to come near the end.

Sometimes Latin can form alternative questions without utrum, but utrum ... an is a very clear and standard way to express whether ... or ....

In a teaching sentence like this, utrum is especially helpful because it signals immediately that an indirect either/or question is coming.

So while Latin can sometimes vary, here utrum is both correct and expected.

A direct version would be something like:

Convivae lac an vinum recipere volunt?
= Do the guests want to receive milk or wine?

Or, if asked directly to them:

Lac an vinum recipere vultis?
= Do you want to receive milk or wine?

Comparing the direct and indirect versions helps:

• direct: volunt / vultis = indicative
• indirect: velint = subjunctive

That change is one of the key things this sentence teaches.