2. Consider the following satisfiability problem: Fred, Daphne, Shaggy, Velma and Scooby are going to order a pizza. First, they need to agree on some toppings. Scooby, as a dog, is happy to eat any toppings. The other members of the group, however, are humans and as such, they have extreme pizza topping preferences. They will order a pizza that can have 1, 2 or 3 toppings, and the entire pizza must have the same topping(s) on all portions of it (it can't be part pepperoni and part cheese, for example) The gang's preferences are i. Shaggy wants a pizza with pepperoni, or with no mushrooms ii. If the pizza has anchovies, then Velma wants no pepperoni Daphne wants mushrooms if and only if there is cheese or anchovies (and both cheese and anchovies would be acceptable too) iv. Fred does not want cheese on the pizza Let Z(x) represent the propositional function "the pizza must have topping x", where the domain for r is the set of possible pizza toppings: cheese (C), mushrooms (M), pepperoni (P) and anchovies (A) Note that statements such as "Shaggy wants a pizza with pepperoni" does not imply that Shaggy wants no other toppings. For example, Shaggy would be perfectly happy with a pepperoni and mushroom pizza (a) Translate each of the group's pizza topping requirements i-iv from English into a proposition using the given propositional function. (b) Are the group's pizza topping requirements satisfiable? If they are, provide a set of pizza toppings that satisfies the requirements. If they are not, provide a concise written argument explaining why not. Do not use a truth table. (c) What pizza topping should we have included that we did not