people liars or trustworthy

Question

I have a visitor that meets A and B.We have trustworth and liars. A declares that he is like B. B declares that one of them is only trustworth.

So I have solved this exercise with truth table

A: trustworthy so p B: trustworthy so q (cause he is saying that one of them is trustworth) I have the table

p        q       p  ^ q
true    true      lie
true     lie      lie 
lie      true     lie
lie      lie      true

from their statement we have true and true so both of them are liars.What the visitor assume ?

1)A and B trustworth 2)A trustworth and B liar 3)A liar and B trustworth 4)both liars

I find 4.both liars is it?

Welcome to MSE. Please read this text about how to ask a good question. — José Carlos Santos, Jan 20 '21 at 07:34
If both are liars then it would mean that either 0 or 2 of them are trustworthy (B) and it would mean that A is not like B, i.e. exactly one is trustworthy, therefore they can't both be liars as it leads to a contradiction — user619755, Jan 20 '21 at 08:19
The answer is that A is a liar and B tells the truth. Your truth table does not answer the question — user619755, Jan 20 '21 at 08:21

score 2 · Accepted Answer · answered Jan 20 '21 at 09:06

As @user619755 said, you can see:

If A is trustworthy, so it said the truth, therefore B become trustworthy like it and say the truth only, but it contradict with its statement, since there is 2 trustworthy, hence A can't be trustworthy.

If B is liar, its statement become wrong, so A can't be trustworthy, therefore it also its statement become wrong, but it contradict with both of them being like each other (liar), hence B can't be liar.

Now the only condition remains:

A is liar and B is trustworthy, So they aren't like each other, as we expect from liarness of A, also there is just one trustworthy, as we expect from trustworthiness of B. Conditions are compatible. So it's the answer.

Already when we know that A can't be trustworthy, it follows that "B is like A" is false, hence B must be trustworthy — Hagen von Eitzen, Jan 20 '21 at 09:20
@HagenvonEitzen You are right, but I prefer to show every one directly, although you solution is shorter and better in some way. — Ali Ashja', Jan 20 '21 at 09:23

people liars or trustworthy

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