Question

"A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet two inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel says, “Neither Zoey nor I are knaves.” Can you determine who is a knight and who is a knave?"

Do the above statement in DIMACS CNF file format.? An please explain your answer

This post is just to explain the CNF DIMACS file format to people new to SAT

Boolean Operators
V – OR
^ – AND
¬ – NOT/Negation

Answer 1

lets break the problem and solve it step wise.

Z: Zoey is a knight

M: Mel is a knight

S: Mel is a knave. Then S =∼ M

T: neither Zoey nor I are knaves. Then T = Z ∧ M

Remember that S and T have two sources to get truth values: who said it, and what it was said. Only the two values agree, S or T is a statement. The answer to this problem should make sure that both S and T are statements.

So the answer is:
Mel is a Knave.
Zoe is a Knight.

Let's check our work:

"Zoey tells you that Mel is a knave"
This is the truth (Mel is a knave), which is what we expect, since Zoe is a Knight. Check!

"Mel says, `Neither Zoey nor I are knaves."
Since Zoe is a Knight, this is a lie. But Mel is a Knave, so he is expected to lie. Check!

HOPE YOU GOT THE IDEA BEHIND THE PROBLEM.