Problem 3: (20 points) Ruh Roh Raggy! Looks like some ghosts are haunting the halls of Gateway South! The Mystery Gang have been called to the scene to unmask who these ghosts are! Here are the facts: There are 15 potential suspects: Aparna, Bella, Colleen, Danielle, Ella, Franklin, Harris, Isabel, Jakob, Jessica, Matthew K., Matthew T., Sanjana, Saoirse, and Sandeep. There are exactly 5 ghosts within Gateway South. When the Mystery Gang splits up to search for clues, they find a list of statements encrypted in logical notation. No one can decipher the statements...besides Scooby Doo, who 4 ate a whole box of Scooby Snacks beforehand and suddenly is able to decipher these logical statements into English. What does Scooby see? Translate each of the 11 statements into English and deduce who these ghosts are, making sure to explain your reasoning in every step of the process: 1. (3x: ghost(x)) ghost(Franklin) 2. (ghost(Saoirse) A ghost (Franklin)) Vx: ghost(x) 3. (ghost(Danielle) A ghost (Colleen)) 4. ghost (Franklin)-ghost (Sanjana) A-ghost (Harris) 5. ghost(Colleen) ghost (Danielle) 6. (ghost(Colleen) V ghost (Matthew T.)) -ghost (Harris) 7. ghost(Matthew T.) ghost (Harris) 8. (ghost(Ella) V ghost(Bella)) 9. ghost(Isabel) -ghost(Aparna) A-ghost(Jessica) 10. (ghost (Matthew K.) V ghost(Jakob)) - ghost(Colleen) 11. -ghost(Sandeep) (-ghost (Jessica) V ghost(Ella))