Math Help - Identify liar/truthful

Hi,
These are the problems I found in a book. I hope someone can help me with this:

1. In an island there are two types of people: liars and truth tellers. When asked a yes/no question, a truth teller always tells the truth and a liar always lies. Then how to ask a single question, that would distinguish between them?

The answer given was ask a question:

"If you are a truth teller than how would you answer the question, 'Are you a liar'?"

The truthful will answer no. And as the truthful has replied yes the liar would reply yes.

My question, independent of the answer of truthful, how does the liar think? What is the response of 'If you are a truth teller' to him ie how does he take the 'if' part into account?

2. Suppose two person - a liar and a truthful - comes to you. Say 1 is A and another is B. Then how to ask a single yes/no question to A to determine whether B is a liar or truthful?

3. Now there are 3 sorts of people: liars, truthful and semi-truthful (part time liar). How to ask a single question to find the type of person?

Originally Posted by amishera

Hi,
These are the problems I found in a book. I hope someone can help me with this:

1. In an island there are two types of people: liars and truth tellers. When asked a yes/no question, a truth teller always tells the truth and a liar always lies. Then how to ask a single question, that would distinguish between them?

The answer given was ask a question:

"If you are a truth teller than how would you answer the question, 'Are you a liar'?"

The truthful will answer no. And as the truthful has replied yes the liar would reply yes.

My question, independent of the answer of truthful, how does the liar think? What is the response of 'If you are a truth teller' to him ie how does he take the 'if' part into account?

i take this to mean that a liar is not a truth teller. so when a liar is asked the question "if you are a truth teller then how would you answer the question, 'Are you a liar'?", the liar would answer yes, because the correct answer to that question is no.

Originally Posted by amishera

2. Suppose two person - a liar and a truthful - comes to you. Say 1 is A and another is B. Then how to ask a single yes/no question to A to determine whether B is a liar or truthful?

"if B is a liar, would he tell the truth?" if A answers no, he is telling the truth, so B is the liar, if he answers yes, he is lying, so B is the truth teller.

comment on answer to 2nd question:
i don't understand the logic behind introducing if's and other conjunctions. when it is given that one is truthful and other is not, a simple question about universal truth like "does sun rise in east" would reveal the fact

Originally Posted by integerfan

comment on answer to 2nd question:
i don't understand the logic behind introducing if's and other conjunctions. when it is given that one is truthful and other is not, a simple question about universal truth like "does sun rise in east" would reveal the fact

i did think about that. however, because question (1) involved asking a question about honesty, i just figured that the answer to question (2) had to be of similar form.