please give me step by step on what each one will say. There is a certain island

Question

please give me step by step on what each one will say. There is a certain island where each resident is either a knight or a knave (but never both). Knights always make true statements and cannot make false statements. Knaves always make false statements and cannot make true statements. In each problem, you talk to a different group of islanders.

A: E is a knave and C is a knight.

B: If C is a knave, then E is a knight.

C: B is a knave and D is a knave.

D: B is a knave and E is a knight.

E says nothing.

Explanation / Answer

If E is a knight, then A is a knave, because he claims E is a knave, B is a knight because the statement p=>q is always true where q is true. Since B says (If C is a knave, then E is a knight) which is a statement of the form p=>q where p='C is a knave' and q='E is a knight' is true, B must himself be a knight (because he cannot say a true statement if he is a knave). C's statement is false since he claims B is a knave and so is D, but we already know that B is a knight. Hence, C cannot be a knight as knight's only say true statements. So, this means C is a knight.

Therefore, the answer is: A=knave, B=knight, C=knave, D=knave, E=knight is the required solution.

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