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 has taken Calculus 1," Q(x) be "x has taken Program Design 1," 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. 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 . c