I am a knave or you are a knight

Question

On the island of knights (always truthful) and knaves (always lying), A says to B:

"Either I am a knave, or you are a knight."

The "or" is inclusive: the statement is true if at least one part is true.

What are A and B?

Accepted Answer

A is a knight and B is a knight. A cannot be a knave. If A were a knave, the first part of the sentence, "I am a knave", would be true, so the whole "or" statement would be true. But knaves never say true things. Contradiction. So A is a knight. Then B is a knight. Since A is a knight, the statement is true. The first part, "I am a knave", is false. For an "or" to be true with a false first part, the second part must be true: B is a knight. The general gadget. "I am a knave or X" is a sentence only a knight can utter, and when a knight utters it, X must be true. So it is a way of asserting X …

I am a knave or you are a knight

Your answer

Discussion

Learn the concepts

Related questions