A&G have a note that carefully differentiates the double questions from a similar alternative—questions featuring the particles aut or vel / -ve. Let’s look at this distinction.
I ask whether he acted unjustly or dishonestly: quaerō num iniūstē aut improbē fēcerit.
I ask whether he acted unjustly or dishonestly: quaerō utrum iniūstē an improbē fēcerit.
In the first question, there are two options on the table, neither of which are necessarily true. It may be that he acted neither unjustly nor dishonestly. In the double question (the second example), it is clear that he either acted unjustly or dishonestly. We have to pick one.
I don’t really like A&G’s example, so here’s another:
I ask whether she likes cats or dogs: quaerō num felēs aut canēs amet.
I ask whether she like cats or dogs: quaerō utrum felēs an canēs amet.
In the first of these two questions, we know nothing about this girl. We’re merely curious about whether she like animals. We might expect our respondent to say something such as, ‘no, she likes birds.’ In the second example, we asking whether she’s a cat-person or a dog-person, assuming she’s either one of the other.
These two types of questions are identical in written English, and differentiable only in stress pattern. In the first question, we would stress ‘ask.’ In the second question, we would stress ‘cats’ and ‘dogs.’
Double Questions, AKA Alternative Questions, are yes-no inquiries, or more broadly, questions with a defined set of responses.
How many jelly beans are on the table? (Question)
Did you see him at the pool hall? (Double Question)
Did you see Juan, Julio or Fernando in the pool hall? (Double Question)
In English, we design double questions with the auxiliary ‘do/did/have + past participle,’ but in Latin, we design double questions with a pair of interrogative particles.
Utrum or -ne will stand in the first-word position (-ne is an enclitic ending for the first word)
An, anne (or) will stand in the second-word position
Annōn or necne (or not) will stand in the final-word position
Is it that you don’t know, if turtles can fly: utrum nescīs, an testūdinēs volāre possint?
Did you desert Lucius Domitius, or did Domitius desert you: vōsne L. Domitium an vōs Domitius deseruit?
Shall I speak with Gabinius, or Pompey or both: Gabīniō dīcam anne Pompeiō an utrīque?
I ask, are these your words or not: quaerō, sint haec tua verba necne?
Note that in the third example, we see anne, which is actually quite rare. In the fourth, we see necne within an indirect question, where is it far more common than in a direct question. Also, note that the third and fourth questions feature an omission of the first of two particles, which is a fairly common omission.
Where an stands alone in the first position, we get a jolt of indignation or surprise:
Are you getting your hair dyed or not: an comās tingis annōn?!