5. Consider the following satisfiability problem: The Scooby Doo gang: Fred, Daphne, Shaggy, Velma, and Scooby are going on vacation. However, before they can book their travel, they need to all agree on where to go. Their trip may involve one or more destinations. They must all travel together to all of the places as one group (so part of the group cannot go to one location while the others go somewhere else i Shaggy wants to go to Venice, or not to Shanghai. ii If the gang goes to Paris, then Velma does not want to go to Venice. iii Daphne wants to go to Brussels if and only if the gang also goes to London and Paris. iv Fred does not want to go to Paris. v Scooby just wants to leave the house and does not care where the gang goes. Let T(z) represent the propositional function "the trip must include destination x, where the domain for r is the set of possible travel locations: Venice (V), Shanghai (S), Paris (P), Brussels (B), and London (L). Note that statements such as "Shaggy want to go to Venice" does not imply that Shaggy only wants to go to Venice. For example, Shaggy would be perfectly happy going to Venice and Shanghai (a) Translate each of the group's travel requirements i - iv from English into a proposition using the given propositional function. [No need to translate Scooby's wishes!] (b) Are the group's travel wishes satisfiable? If they are, provide a list of destinations that satisfies the requirements. If they are not, provide a concise written argument explaining why not. Do not use a truth table (c) What travel destination should we have included in the lst? [Note, this is for fun.]