Part I: Proving an argument is valid using rules of inference (30 pt.) 1. (30 pt.) Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid. Let S(x) be "x is a student in this class," P(x) be "x has access to Gradescope," and Q(x) be "X can submit the homework assignment," where the domain consists of all people. Every student in this class has access to Gradescope. Everyone who has access to Gradescope can submit the homework assignment. Ana is a student in this class Therefore, Ana can submit the homework assignment. a. Let S(x) be x is a student in this class," P(x) be"x knows how to write programs in Java," and Q(x) be"x can get a goodjob," where the domain consists of all people. Bob, a student in this class, knows how to write programs in Java. Everyone who knows how to write programs in Java can get a good job. Therefore, someone in this class can get a good job. b. Let P(x) be x has taken CS 109." Q (x) be x has taken CS 1 1 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 CS 111 or CS 109. Every student who has not taken CS 111 but has taken CS 109, 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 CS 111. c