# Find the liar and the reliable

I have two categories of people, the reliable and the liars.The reliable telling always the truth,the liars always telling lies. One visitor meets both of them:

A declares: "I and B are the same." B declares : "From us, only one is reliable."

What situation is true?

a)both are liars
b) the A is liar and the B reliable
c)both reliable
d)A and B reliable

• Please finish the problem statement. It seems incomplete. – Matti P. Jan 19 at 12:10
• ok moment I will give you some answers to chose – maik kain Jan 19 at 12:11
• @MattiP. better now? – maik kain Jan 19 at 12:12
• I don't understand the sentence "what the visitor will have" ? Perhaps the final question should be: "Which of the following propositions is true?" – Matti P. Jan 19 at 12:14
• yes thats right ,sorry my english are not good :) – maik kain Jan 19 at 12:18

## 2 Answers

A and B cannot be in the same category, since -

1. if A and B are both liars, then A's statement ('I and B are the same') is true. But A is a liar, so A will always speak falsehoods, and not true statements, thus A and B cannot be both liars.
2. if A and B are both reliable, then B's statement ('From us, only one is reliable') is false. But B is reliable, therefore B cannot speak falsehoods, only truths, thus A and B cannot be both reliable.

That eliminates options a, c, d from your list, leaving option b.

If A is liar and B is reliable - then A's statement ('I and B are the same') is false, and B's statement ('From us, only one is reliable') is true. Since A can only speak lies and B can speak only truths, this is a valid situation.

If A is a liar then A and B are not the same hence B is a reliable. Then B says one one of us is reliable hence pointing to himself. Therefore the statement is true.

However if A is reliable then both B and A the same contradicting B's statement of only one reliable between both of them. Contradiction.

Hence A is a liar and B is reliable B is the answer. Talk about 'there is one imposter among us.'