There exist two islands somewhere in the Bermuda Triangle (why not ?).  On Verity Island, everyone speaks the truth all the time.  On Sophist Island, everyone lies all the time.  The natives of each island despise normal people, like you, who can lie or tell the truth at will, so they speak a different language to be as confusing as possible.

EDIT (Part III): Due to recent advancements in technology, the Veritians and the Sophists are able to travel from island to island.

One day, your plane crashes on one of the islands.  You are well versed in Bermuda folklore (of course you are ), so you realize what happened.  First, you must determine which island you are on.  However, the natives will respond in a different tongue, in which "yes" and "no" are "boo" and "moo", but you do not know which.  If you can only ask one question, what should it be?

(There is more than one correct answer)

~ Flying2828 °·°

Solution ?

"If I asked someone from the other island if you were telling the truth, what would they say?". The answer denotes "No".

SPOILER ALERT

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How about, "What is the opposite of boo?" If they reply with "moo," you are on Verity Island, if they tell you "boo," you are on Sophist Island.

Is this correct?

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END OF SPOILER

Hmmm, the logic here is flawed.

I'd fire up the grill, because anything that says, "Moo," is obviously a cow. And, hey, I really like steak.

Artfizz, although your answer successfully isolates the yes and no of their language, that is not the goal.  But good job!

Philidor_position, that is correct!  Anything of that nature would work.

Bananacake, as charming as that is, remember that these natives are savage .

Anyway, you have completed part 1!  Yay!!!  Artfizz completed what would have been part 2 (a much simpler solution would have been "Are you a Veritian?" to which they would have replied yes), so I suppose we are now on part 3 .

Due to recent advancements in technology, the Veritians and the Sophists are able to travel from island to island.  All previous rules apply, and you still have the same goal: determine which island are you on!

Good luck!

~ Flying2828 °·°

Come on...  No one can get it???  How about you split it into cases..?

KEY:

E: on Verity Island

O: on Sophist Island

V: speaking to Veritian

S: speaking to Sophist

Y: moo = yes

N: moo = no

Possibilities:

a) EVY      ESY     EVN     ESN

b) OVY     OSY     OVN     OSN

"Simply", formulate a question that has the cases in (a) have the same response and that has the cases in (b) have the same response.

Do you need another hint?

Can they travel individually? I mean, have the communities mixed together on both islands? Or do they travel only as whole groups?

boo

Philidor_position, sorry about the delayed response.  The communities have mixed together!  People could travel as individuals or in groups: it does not matter.

Yes, InevitableConclusion, I am making it harder .

The solution is: "What does a cow say?"