Lucia rogat utrum hoc pronomen demonstrativum sit an relativum.

Because utrum ... an introduces an indirect question, and in Latin indirect questions normally take the subjunctive.

So:

• est = indicative, is
• sit = subjunctive, may be / is in an indirect-question context

After rogat (asks), Latin does not usually say something equivalent to whether it is with the indicative. It uses the subjunctive:

• Lucia rogat ... sit ... = Lucia asks whether ... is ...

This is a standard rule of Latin syntax.

utrum ... an means whether ... or.

It sets up a choice between two alternatives:

• utrum ... sit
• an ...

So here the structure is:

• utrum hoc pronomen demonstrativum sit an relativum
• whether this pronoun is demonstrative or relative

A helpful way to remember it is:

• utrum = whether
• an = or

Because an is the normal word used for the second part of a two-part alternative in questions.

Latin distinguishes between:

• ordinary or joining words or clauses: aut, vel
• or in a question with alternatives: an

So after utrum, Latin normally uses an:

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

That is why an relativum is correct here, not aut relativum.

It is nominative neuter singular.

Here hoc pronomen is the subject of sit:

• hoc pronomen ... sit
• this pronoun is ...

Why neuter singular?

• pronomen is a neuter singular noun
• hoc agrees with pronomen in gender, number, and case

So:

• hoc = nominative neuter singular of hic, haec, hoc
• pronomen = nominative neuter singular

Because hoc must agree with pronomen, and pronomen is neuter.

The forms are:

• hic = masculine singular
• haec = feminine singular
• hoc = neuter singular

Since pronomen is neuter, the correct form is:

• hoc pronomen = this pronoun

Because they agree with pronomen, which is neuter singular.

They are adjectives here:

• pronomen demonstrativum = a demonstrative pronoun
• pronomen relativum = a relative pronoun

Since pronomen is neuter singular nominative, both adjectives must also be:

• demonstrativum
• relativum

So the agreement is:

• hoc pronomen demonstrativum
• hoc pronomen relativum

All the describing words match pronomen.

Grammatically, demonstrativum and relativum are best understood as predicate adjectives with pronomen:

• hoc pronomen demonstrativum sit an relativum
• whether this pronoun is demonstrative or relative

So the main idea is not merely whether hoc is demonstrative or relative, but rather:

• whether this pronoun belongs to the demonstrative or relative type

Latin often uses an adjective this way after a form of esse:

• pronomen demonstrativum est = it is a demonstrative pronoun
• pronomen relativum est = it is a relative pronoun

Because Latin does not use a word like English that here. Instead, it uses an indirect question.

English says:

• Lucia asks whether this pronoun is demonstrative or relative.

Latin says:

• Lucia rogat utrum ... an ...

The entire utrum ... an clause functions as the object of rogat. So Latin does not need an extra word meaning that in this sentence.

Latin word order is much freer than English word order because Latin shows grammatical relationships mainly through endings, not position.

English strongly prefers:

• Lucia asks whether this pronoun is demonstrative or relative.

Latin can place words more flexibly:

• Lucia rogat utrum hoc pronomen demonstrativum sit an relativum.

A few things to notice:

• rogat comes early, introducing the main action
• utrum signals that a question clause is beginning
• hoc pronomen comes before sit
• demonstrativum and relativum are placed near the contrast they express

So the word order is natural Latin, even if it does not match English exactly.

Sometimes Latin can omit utrum in indirect questions, especially when the meaning is clear from context, but utrum ... an is a very clear and standard way to present two alternatives.

So with both options stated, utrum ... an is especially neat and explicit:

• utrum ... demonstrativum sit an relativum

It clearly tells the reader:

• there are two possibilities
• the speaker is asking which of the two is true

rogat is the main verb of the sentence and means asks.

Its subject is Lucia:

• Lucia rogat = Lucia asks

What is she asking? The entire indirect question:

• utrum hoc pronomen demonstrativum sit an relativum

So the structure is:

• main clause: Lucia rogat
• dependent clause: whether this pronoun is demonstrative or relative

This is a very common Latin pattern:

• verb of asking, knowing, wondering, etc.
• followed by an indirect question in the subjunctive