Answer to Question #270926 in Discrete Mathematics for mirsha

Question

Suppose that you meet three people Aiman, Borhan, and Camelia. Can you determine what Aiman, Borhan, and Camelia are if Aiman says "All of us are knaves" and Borhan says "Exactly one of us is a knave."?

Answer 1

Let us assume that,  Aiman says "All of us are knaves" is true.

So, Aiman is a knave.But we know that knave always tell the lie.

Our assumption is wrong.

So, Aiman is a knave and at least one among Borhan and Camelia is a knight.

Let us assume that Borhan is a knight. Then his statement "Exactly one of us is a knave" is true. Hence in this case Aiman is a knave, Borhan is a knight and Camelia is a knight.

Let us assume that Borhan is a knave. Then his statement "Exactly one of us is a knave" is false. Hence in this case Aiman is a knave, Borhan is a knave and Camelia is a knight.

Therefore we know that Aiman is a knave and Camelia is a knight. But Borhan may be a knave or knight. We cannot determine exactly.