10 points) [Solve using a DLV program] Game II: Orange and Purple (Source: Alice in Puzzle Land: A Carrollian Tale for Children Under Eighty by Raymond Smullyan) "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 cas