Problems with probably very simple logic question

[Hypnos_16]

Homework Statement

The Island of Knights and Knave, where knights never lie; knaves lie always (that is, every statement made by a knight is rue, every statement made by a knave is false).

a) Suppose you meet two islanders and ask who they are. One of them says "if i am a knight then so is my friend." Can you tell who is who

b) Your friend asked an island "do you ever answer 'no' to questions?" You didn't hear the answer (yes/no) but your friend says that now she knows for sure whether the islander was a knight or a knave. Can you tell what the answer was and whether the island was a knight or knave?

Homework Equations

Part A. is causing the most grief, i have a basic idea, but I'm just not sure about it.
So let's say the islander are A and B then we assign values
P = A is a Knight
Q = B is a Knight
(or so i think)

The Attempt at a Solution

I reasoned with myself that i want to see if A is a knight
so, if A is knight, then so is b

(P ----- > Q)

if that's correct, and A truly is a knight, then we can say

(P ----- > Q) <-----> P

So then i made a truth table, which is kind of hard to post in here, but i did get a single thing being true at the end. That the top line was True, meaning that both A and B are true, both a knights. After reviewing some work however, i saw that someone answered a similar question about "At least one of us is a knave." They used nots in theirs but basically the rest was unchanged, they came up with that A was a knight and B wasn't. That worried me, I'm basically looking for any reassurance that what i did here was right. Logic is still sort of new to me

Part B.

"If your friend asked an islander if they answers no to questions, then the liar would say “no,” and a truthful man would say “yes.” Therefore, if the man says “yes,” then he is surely telling the truth and must be a Knight, and if he says “no,” breaking the rule of answering with no, then he must be a Knave"

That was my response to part B. Does that make any since?

Thanks for the help in advance (if i find anyone willing to read all that and help)

 

[nate808]

Your reasoning for part A is correct. If A is a knight, then B must also be a knight. This is because a knave can never say that they are a knight, so if B is a knave, then they would have to say that they are a knave, which is false. Therefore, if A is a knight, B must also be a knight.

For part B, your reasoning is also correct. If the islander is a knight, they would answer "no" to the question because they always tell the truth. If the islander is a knave, they would also answer "no" because they always lie. However, since the question asked is whether they ever answer "no" to questions, the knave would have to answer "yes" in order to be consistent with their lying nature. Therefore, if the islander answers "yes," they must be a knight.