Recll that the inhabitants of the Island of Knights and Knav

Recll that the inhabitants of the Island of Knights and Knaves are either knights, who always tell the truth, or kanves, who always lie. While visiting the Island you encounter... ...two inhabitants, A and B, who tell you the following: If B is a knave then I\'m not a knight. One of us is a knight and the other is a knave. Determine, as completely you can, whether each of A and B knight or a knave. [3]

Solution

a) There are only 4 cases as only both A and B are knight or knave or one of them is knigh and other knave
1. Both are Knight -> that means both are saying truth which means B is saying truth which contradicts that both are knight So this is not possible.
2. Both are knave -> so that means both are saying lie so whoch contradicts A statement so this is not possible
3. A is knight B is knave -> in this also A statements contradict our assumption so not possible
4. A is knave B is knight-> a is lying that B is knave and B is saying truth So this case is valid
b) E is knight as if E is knave that means C is knight which contradicts B and F statements so also as per E
   C is knave
   B is knight
   F is knave
G is knight
   D is knight
A is knave