$2.(10$ points$)[$Solve using a DLV program$]$

"Now," Tweedledum continued, "one or both of us will come out of the house, each carrying either an orange or purple card, and he $($we$)$ will make statements. Then you are to figure out who is who.$$

"Just a minute," said Alice, "you have not told me the significance

of the colors orange and purple. Does one of them signify lying and

the other truth$-$telling? And if so$,$ which color means which?$$

$"$Ah$,$ that's the most interesting part of the game!" said

Tweedledum. "You see, when I carry an orange card, it means

that I am telling the truth, and when I carry a purple card, it means

I am lying!$$

"Contrariwise," said Tweedledee, "when I carry an orange card, it means I am lying, and when I carry a purple card, it means I am telling the truth!$$

On the next round, both brothers came out and made the following statements:

FIRST ONE: Our cards are of the same color.

SECOND ONE: Our cards are not of the same color.

Did the first or second person tell the truth?

$[$Hint: we need to know if first or second person told the truth. We did not ask what color are the cards, or WHO the first speaker is$.$ Each speaker is different. Each carries only one card. Note that compared to Knight$/$Knave problems we $($a$)$ don$$t know the speaker name $($b$)$ both

could either be liars or truth tellers, depending on the card color.

So you need to consider $4$ cases for each speaker $($either Dum or Dee, and either purple or

orange$).$ There may be more than one model of these sentences, but only one answer to the

question.

Use the DLV ASCII formula format