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

1. ## [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

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.

2. Hello TGS
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

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 $\displaystyle a$ be the proposition "A is a knight", and $\displaystyle b$ be the proposition "B is a knight"

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

Therefore $\displaystyle a\Rightarrow b$

Therefore $\displaystyle a\Rightarrow$ B tells the truth

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

Therefore $\displaystyle a$ is false, and A is therefore a knave.

Now $\displaystyle \neg b \Rightarrow$ B always lies

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

Therefore $\displaystyle \neg b$ is false. Therefore B is a knight.