Consider the following satisfiability problem: fred, daphne, shaggy, velma and scooby are going to a movie, and they find a set of four seats in the front row for them to sit (scooby is happy to lounge at their feet). some of the people in the group are bickering and thus don't want to sit next to each other. others are good friends and do want to sit next to each other. in particular i. shaggy wants to sit next to daphne or velma ii. velma wants to sit next to daphne, but refuses to sit next to shaggy or fred ii. if daphne doesn't sit next to fred, then velma wants to sit next to fred iv. fred wants to sit next to daphne if and only if daphne does not sit next to shaggy let n(x, y) represent the propositional function "z and y are sitting next to one another", where the domain for r and y is the set {f, d, s, v]. note that this propositional function is symmetric, in the sense that n(x, y) is true if and only if n(y, x) is true. for instance, if fred and velma sit next to each other, then the propositions n(f, v) and n(v, f) are both true. (a) translate each of the group's seating requirements i-iv from english into a proposition. (b) are the group's seating requirements satisfiable? if they are, provide a seating arrangement that satisfies the requirements. if they are not, provide a concise written argument explaining why not