Follow the instructions

Task 5 - A Guide to Proper Manners and Predicate [16 pts] Let the domain of discourse be course staff and hobbies. Define the predicates Staff(x) to mean that x is a member of the course staff and Hobby(y) to mean that y is a hobby. Define the predicate Enjoys(x, y) to mean that a enjoys y (presumably a is a person and y is a hobby) and the predicate RequiresSkill(y) to mean that y requires skill (presumably y is a hobby). Translate each of the following logical statements into English. You should not simplify. However, you should use the techniques shown in lecture for producing more natural translations when restricting domains and for avoiding the introduction of variable names when not necessary. a) -3y (Hobby(y) / RequiresSkill(y)) b) 3x ( Staff(x) ^ By (Hobby(y) ~ Enjoys(x, y)) ) c) 3x ( Staff(x) ~ By (Hobby(y) ^ Enjoys(x, y) ^ - RequiresSkill(y))) d) Vy ((Hobby(y) ^ RequiresSkill(y)) - 3x (Staff(x) ^ Enjoys(x, y) ) ) Task 6 - Animal, Vegetable, or Literal [12 pts] Let P and Q be predicates. a) Translate the proposition ((*)0 - (x) d) IA directly into English. This time, do not try to make your translation natural sounding. Just do the most literal translation possible. b) Translate the proposition (VI P(x)) - (Vx Q(x)) directly into English. Again, do not try to make your translation natural sounding. Just do the most literal translation possible. c) Give an example of predicates P and Q and a domain of discourse so that the propositions from parts a and b do not have the same truth value (i.e., one is false and one is true). d) Give an example of predicates P and Q and a domain of discourse where the propositions from parts a and b do have the same truth value (i.e., both are false or both are true)