# [SOLVED] Knights and Knaves help &gt;__&lt;

• Sep 29th 2009, 04:07 PM
TGS
[SOLVED] Knights and Knaves help &gt;__&lt;
Two natives A and B address you as follows:

A says: Both of us are knights.
B says: A is a knave.

What are A and B?

Okay, so I assume that A is telling the truth so:

(a ^ b)

and since B is a knight then what B says has to be true so:

~a

Then there's the contradiction:

a ^ ~a

The negation law states:

c

...and that's how far I got.. -____-

I don't even know if I'm doing this correctly.
• Sep 30th 2009, 04:42 AM
Hello TGS
Quote:

Originally Posted by TGS
Two natives A and B address you as follows:

A says: Both of us are knights.
B says: A is a knave.

What are A and B?

Okay, so I assume that A is telling the truth so:

(a ^ b)

and since B is a knight then what B says has to be true so:

~a

Then there's the contradiction:

a ^ ~a

The negation law states:

c

...and that's how far I got.. -____-

I don't even know if I'm doing this correctly.

I assume that a knight always tells the truth and a knave always lies.

So let $a$ be the proposition "A is a knight", and $b$ be the proposition "B is a knight"

Then $a \Rightarrow (a\land b)$, since A says "Both of us are knights"

Therefore $a\Rightarrow b$

Therefore $a\Rightarrow$ B tells the truth

Therefore $a\Rightarrow \neg a$, since B says "A is a knave".

Therefore $a$ is false, and A is therefore a knave.
Now $\neg b \Rightarrow$ B always lies
Therefore $\neg b \Rightarrow a$, since B says "A is a knave"
Therefore $\neg b$ is false. Therefore B is a knight.