Use DLV to solve the

following problem from HW#$3.$ For DLV programs, remember to turn in the program $($a text file$)$ as well as the documentation $($what you intend propositions mean, you can do this as comment within the program$)$ and the output $($and what the output means$)$

There are exactly two types of people on an island: Truth tellers always tell the truth. Liars always lie. You meet two people, Bill and Kim.

Bill says: $$We are both liars.

$($a$)$ Represent what you know in propositional logic as a DLV program

$($b$)$ Show $($using DLV$)$ that there is only one model of this sentence.