3 On the Island of Knights and Knaves you meet two natives A

3. On the Island of Knights and Knaves you meet two natives, A and B. Given their statements below, what can you determine about their identities? Fully explain your
reasoning in words
(a) B says: \"I am a knight only if A is a knight\". What do you conclude?
(b) B says: \"I am a knight or A is a knight\". What do you conclude?
(c) In Case (b) above, what do you conclude if A adds: \"I am a knave if and only if B is a knight\"?

Solution

We are given that

On the Island of Knights and Knaves you meet two natives, A and B

(A)

B says: \"I am a knight only if A is a knight\"

If it is true , then A = knight and B=knight...which is not possible

But if B is lieing , then we get

B is knave ... but A can be knight....which can be possible

Hence , B is lying ..................Answer

(B)

B says: \"I am a knight or A is a knight\"

If A = knight then it is true .....it can be said by knight
If both are knaves then it is false

(C)

B says: \"I am a knight or A is a knight\"

A adds: \"I am a knave if and only if B is a knight\"

If it is true ... Then B is knight ... A may be knight or knave

But from second statment

It is possible that

B is knight and A is knave ...........Answer