On a fictional island all inhabitants are either knights who

On a fictional island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie. You arrive on the island and come across two natives named Alice and Bob. Alice says: “If Bob is a knave, then I am a knave.” What are Alice and Bob?

Solution

We need to consider two cases:

frist case: Alice is a knight.

then, Bob cannot be a knave. Both are knight.

Second case: Alice is a knave.

Then,\" if Bob is a kanve, I am a knave\" this statement is true but, since Alice is a knave, she must be lying, so there is a contradiction.

These together impliy that both Alice and Bob are knights.