Answer to Question #259478 in Discrete Mathematics for lola

Question

A says “If B is a knight, then I am a knave”, B says nothing.

Answer 1

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

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

p∧∼q

but since B is knight, p∧∼q

p∧∼q becomes false.

So only possible answer is (A).