[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

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

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".