Is this a correct solution to determining which of two people is the liar using one question?

Question

I am a newbie to Stack-Exchange and if there is any problem in my question -- I apologize beforehand .

I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen , when I came across the following question :

An explorer is captured by a group of cannibals. There are two types of cannibals—those who always tell the truth and those who always lie. The cannibals will barbecue the explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He is allowed to ask the cannibal exactly one question.

Find a question that the explorer can use to determine whether the cannibal always lies or always tells the truth.

My Solution :

If I were to ask you whether you are a liar, would you answer yes?

• The honest person would say NO.
• The liar would say YES (due to double negation).

Doubt :

Am I correct in saying my answer will work? It almost seems too simple.

Answer 1

You have exactly the right idea. You force the liars to make two negations. This question works just fine, as will others, as long as they are "honest" liars.

Answer 2

The gist of the answer is to actually ask a question within a question.

Let's break down the following revealing question:

"If I were to ask you whether you are a liar, would you answer yes?"

Here, indeed, we have two questions that are:

1. Are you a liar
2. Would you answer yes to question 1?

By asking the second question, the liar is revealed. The honest would not respond differently. Let's take a look by asking these two questions to the two cannibals.

ASKING THE LIAR:

1. Are you a liar?

• Honest answer (he wouldn't say this): YES
• Actual answer (negation of honest answer): NO

2. Would you answer yes to question 1?

• Honest answer (he wouldn't say this): NO
• Actual answer (negation of honest answer): YES

ASKING THE THRUTFUL:

1. Are you a liar?

• Honest answer: NO
• Actual answer: NO

2. Would you answer yes to question 1?

• Honest answer: NO
• Actual answer: NO

So the honest cannibal will say NO consistently, whereas the liar will lie about a lie, which will reveal him.

Answer 3

Well I think this will also work-"if I can find whether you are a liar or truther will you stop barbecue me?"
Liar will say No.
Truther will say yes.