A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.
You meet four inhabitants: Bozo, Marge, Bart and Zed.
- Bozo says,"
Bart and Zed are both knights". - Marge tells you that both Bart is a knight and Zed is a knave
- Bart tells you,"
Neither Marge nor Zed are knaves". - Zed says that neither Bozo nor Marge are knaves.
Can you determine who is a knight and who is a knave?
I am having extreme difficulty with this can anyone help me?
I assume is starts like this.
So
$Bo\equiv(Ba\land Ze)$
$Ma≡(Ba\land \lnot Ze)$
$Ba\equiv(Ma\lor Ze)$
$Ze≡(Bo\lor Ma)$
Where
$Bo$= Bozo is a knight
$Ma$= Marge is a knight
$Ba$= Bart is a knight
$Ze$= Zed is a knight
Best Answer
First, your symbolic translations of Bart’s and Zed’s statements are incorrect. Bart actually said $$\text{Ma}\land\text{Ze}\;,$$ and Zed said $$\text{Bo}\land\text{Ma}\;.$$
A quick way to solve it is to suppose that Bart is a knight. Then he’s telling the truth, so Marge and Zed are also knights. But that’s impossible, because Marge said that Zed is a knave: if she’s a knight, she’s telling the truth, and Zed isn’t knight. Thus, Bart cannot be a knight and must therefore be a knave. Can you finish it from there?