Prove that the given argument is valid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. Then use the rules of inference to prove that the form is valid.

(a)

The domain of discourse is the set of musicians in an orchestra.

Everyone practices hard or plays badly (or both). Someone does not practice hard. Someone plays badly.

(b)

The domain of discourse is the set of people who live in a city. Linda lives in the city.

Linda lives in the city. Linda owns a Ferrari. Everyone who owns a Ferrari has gotten a speeding ticket. Linda has gotten a speeding ticket.

(c)

The domain of discourse is the set of all paintings.

All of the paintings by Matisse are beautiful. The museum has a painting by Matisse. The museum has a beautiful painting.

(d)

The domain is the set of students at an elementary school.

Every student who has a permission slip can go on the field trip. Every student has a permission slip. Every student can go on the field trip.

(e)

The domain of discourse is the set of students at a university.

Larry is a student at the university. Hubert is a student at the university. Larry and Hubert are taking Boolean Logic. Any student who takes Boolean Logic can take Algorithms. Larry and Hubert can take Algorithms.