Magistra rogat utrum sententia discipulae exemplum bonum ostendat an culpam.

Utrum ... an introduces an either/or question. Here it means whether ... or.

So:

• utrum = whether
• an = or

In this sentence, the teacher is asking between two possibilities:

• exemplum bonum = a good example
• culpam = a fault

So utrum ... an sets up the choice: whether the sentence shows a good example or a fault.

Because the clause introduced by utrum ... an is an indirect question, and Latin normally uses the subjunctive in indirect questions.

The main clause is:

• Magistra rogat = The teacher asks

What she asks is then expressed indirectly:

• utrum sententia discipulae exemplum bonum ostendat an culpam

Since this is not a direct question like Ostenditne...?, but a reported/embedded question after rogat, Latin uses ostendat rather than ostendit.

The subject is sententia.

Why?

• sententia is nominative singular
• ostendat is singular
• the meaning fits: the sentence shows...

So the structure is:

• sententia = the sentence
• ostendat = shows / may show

Together: the sentence shows

Here discipulae is most naturally genitive singular, meaning of the student or the student's.

So:

• sententia discipulae = the student's sentence

This is a very common Latin way to show possession.

A learner may notice that discipulae could also be dative singular, nominative plural, or vocative plural in other contexts. But here the genitive makes the best sense because it is attached to sententia and expresses ownership.

They are in the accusative because they are the things being shown by ostendat. In other words, they function as objects of the verb.

• exemplum bonum = a good example
• culpam = a fault

The verb ostendere often takes a direct object: to show something.

So the sentence asks whether the student's sentence shows:

• a good example or
• a fault

Because Latin does not need to balance the two alternatives with exactly the same kind of phrasing.

The two choices are simply:

• exemplum bonum = a good example
• culpam = a fault

Latin is perfectly happy to make one option more specific than the other. There is no grammatical problem here. The teacher is asking whether the sentence is showing something positive, a good example, or something negative, a fault.

Because Latin word order is more flexible than English word order.

• exemplum bonum
• bonum exemplum

Both can mean a good example, as long as the adjective agrees with the noun.

Here they agree in:

• gender: neuter
• number: singular
• case: accusative

So bonum matches exemplum, and the order does not change the basic meaning.

Because an is commonly used in questions, especially after utrum, to introduce the second alternative.

So:

• utrum X an Y = whether X or Y

This is different from a simple coordinating or in a statement. In this sentence, an belongs to the question structure itself.

That is why utrum ... an is the natural pairing here.

Not in the same way.

• aut and vel are ordinary conjunctions meaning or
• an is specifically used in question structures, especially with utrum

So if the sentence is asking whether this or that, utrum ... an is the idiomatic pattern.

A native English speaker may want to translate all of them as or, but Latin distinguishes ordinary coordination from question alternatives more clearly.

It breaks down like this:

• Magistra rogat = The teacher asks
• utrum ... an ... = whether ... or ...
• sententia discipulae = the student's sentence
• exemplum bonum ostendat = shows a good example
• an culpam = or a fault

So the skeleton is:

• [Main clause] The teacher asks
• [Indirect question] whether the student's sentence shows a good example or a fault

This is a very common Latin pattern: a verb of asking followed by an indirect question in the subjunctive.

Not a normal noun object. Instead, rogat is followed by an indirect question clause.

So rather than:

• The teacher asks a question

Latin gives:

• The teacher asks whether...

That whole utrum ... an clause acts as the content of what is being asked.

English works similarly:

• She asks whether it is correct
• She asks whether the sentence shows a good example or a fault

Because Latin, like English, often leaves out a repeated verb when it is easily understood.

The full idea is:

• utrum sententia discipulae exemplum bonum ostendat an culpam ostendat

But Latin omits the second ostendat because it is obvious from the first half.

English does the same thing:

• whether the sentence shows a good example or a fault

We do not usually repeat shows either.

Yes, sententia can mean several things depending on context, including:

• sentence
• opinion
• judgment
• view

In this sentence, if the meaning has already been provided to the learner as sentence, then that is the intended sense here.

Still, it is useful to know that Latin words often have a wider range of meanings than a single English gloss suggests. Context tells you which one is meant.

Because Classical Latin has no definite article like English the.

So:

• magistra can mean teacher or the teacher
• sententia can mean sentence or the sentence
• culpam can mean a fault or the fault, depending on context

English usually has to choose a/an or the, but Latin often leaves that for the reader to infer from context.

Yes, to a large extent.

For example, Latin could rearrange the words and still keep the same basic meaning because the endings show the grammatical roles. For instance:

• Magistra rogat utrum discipulae sententia exemplum bonum ostendat an culpam.

This would still mean essentially the same thing.

However, word order can affect emphasis. The version you have places sententia discipulae early in the indirect question, which keeps the focus clearly on the student's sentence.