Nptel

Question

A certain country is inhabited only by people who either always tell truth or always lies, and who will respond to a question only with yes or no. A tourist come to fork in road, where left branch leads to capital and other does not. There is no sign indicating which branch to take. but there is an inhabitant, Mr Z standing at the fork. What single Yes/No question should tourist ask him determine the branch to take?

• A. It is true that you are the truth teller and the left road leads to capital or you are liar and the right rod leads to capital
• B. If i ask you whether the left road leads to capital, you will say yes, won't you?
• C. If I ask the other kind of person whether the right road leads to the capital, he will say yes won't he ?

Out of $3$ Question above which question can lead you towards capital?

1. A,B
2. B,C
3. A,C
4. A,B,C

Comments

1)A,B

Answer 1

Ans: A,C

Option A :

Mr Z says YES

If answer to the first question is yes, it either means that Mr. Z is a truth teller and he speaks the truth that the left route leads to the capital or it means that he is a liar and he tells the lie that right route leads to the capital

Option C:

Mr Z answers YES

Supposing Mr. Z is truthful, the other type will be a liar ,and that person will tell lies that right road leads to the capital

Now, supposing Mr.Z is a liar ,the other type will be truthful and he will truth fully say right road leads to capital .

(But, Mr Z told lies about this)

Option B:

Mr. Z answers YES

Suppose Mr Z is truthful, he says truth that left road leads to capital.

Suppose Mr. Z is liar ,he says lies that left road leads to capital. (BUT,the left road actually leads to capital)