1. Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid. Indicate the rules of inference used in each step.

Let P(x) be "x is a student in this class," Q(x) be "x owns a convertible," and R(x) be "x has gotten at least one speeding ticket," where the domain consists of all people.

a. Matt is a student in this class. Matt owns a convertible. Everyone who owns a convertible has gotten at least one speeding ticket. Therefore, someone in this class has gotten a speeding ticket.

Let P(x) be "x is a student in this class," Q(x) be "x owns a personal computer," and R(x) be "x can use a word processing program," where the domain consists of all people.

b. Every student in this class owns a personal computer. Everyone who owns a personal computer can use a word processing program. Kate is a student in this class. Therefore, Kate can use a word processing program.

Let P(x) be "x has taken Calculus I," Q(x) be "x has taken Program Design I," and R(x) be "x has permission from the instructor to enroll in this class," where the domain consists of all students in this class.

c. Every student in this class has taken Calculus I or Program Design I. Every student who has not taken Calculus I but has taken Program Design I, has permission from the instructor to enroll in this class. Therefore, every student who does not have permission from the instructor to enroll in this class has taken Calculus I.