The Answer to the Question
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Knights always tell truth while Knaves always tell lie.
The given implication is
if B is a Knight then I am a Knave be denoted as
p: B is a knight
q: I am a knave (Means A is a knave)
p→q is our given implication
(A) A is a knight and B is a knave If A is knight, then we can take the given implication as said by A in it's original form since Knights always tell truth but then if B is a knave, then the antecedent of the implication becomes false, there making the implication true so A can be a knave or knight both.
(B) A is knave and B is Knight
If A is knave, then whatever A said need to be complement to get original result since knaves always lie. So complement of p→q
p→q is p∧∼q
p∧∼q which is false as A is knave which makes ∼q
∼q false. So this cannot be our answer.
(C)Both A and B are knight-This will make our implication false. So ruled out.
(D)Both A and B are knave.
So we again need to reverse statement of A and it is p∧∼q
but since B is knight, p∧∼q
p∧∼q becomes false.
So only possible answer is (A).