Express each of these system specifications using predicates, quantifiers, and logical connectives, if necessary.

a) At least one console must be accessible during every fault condition.
b) The e-mail address of every user can be retrieved whenever the archive contains at least one message sent by every user on the system.
c) For every security breach there is at least one mechanism that can detect that breach if and only if there is a process that has not been compromised.
d) There are at least two paths connecting every two distinct endpoints on the network.
e) No one knows the password of every user on the system except for the system administrator, who knows all passwords.[

When you type the pwd command, you notice that your current location on the linux filesystem is the /usr/local directory. answer the following questions, assuming that your current directory is /usr/local for each question. a. which command could you use to change to the /usr directory using an absolute pathname? b. which command could you use to change to the /usr directory using a relative pathname? c. which command could you use to change to the /usr/local/share/info directory using an absolute pathname? d. which command could you use to change to the /usr/local/share/info directory using a relative pathname? e. which command could you use to change to the /etc directory using an absolute pathname? f. which command could you use to change to the /etc directory using a relative pathname?

[java] create an application called registrar that has the following classes: a. a student class that minimally stores the following data fields for a student: - name - student id number - number of credits - total grade points earned and this class should also be provides the following methods: - a constructor that initializes the name and id fields - a method that returns the student name field - a method that returns the student id field - methods to set and retrieve the total number of credits - methods to set and retrieve the total number of grade points earned. - a method that returns the gpa (grade points divided by credits) b. an instructor class that minimally stores the following data fields for an instructor: - name - faculty id number - department the following methods should be provided: - a constructor that initializes the name and id fields - methods to set and retrieve the instructor’s department. c. a course class that minimally stores the following data for a course: - name of the course- course registration code- maximum number of 35 students- instructor- number of students- students registered in the course (an array)the following methods should also be provided: - a constructor that initializes the name, registration code, and maximum number of students- methods to set and retrieve the instructor- a method to search for a student in the course; the search should be based on an id number.- a method to add a student to the course. if the course is hill, then an exception with an appropriate message should be raised (try creating your own exception class for this). also, be sure that the student is not already registered in the course. the list of students should be in the order that they registered.- a method to remove a student from the course. if the student is not found, then an exception with an appropriate message should be raised (use the same exception class mentioned a method that will allow course objects to be output to a file using object serialization- a method that will allow course objects to be read in from a file created with object serializationyou will note that the student and instructor classes described above have some commonality. create aperson class that captures this commonality and uses it as a base class for student and instructor. this class should be responsible for the name and id fields and also provide atostring method that returns a string of the form name, id. this will be the inheritedtostring method for the student and instructor classes.1. draw a uml diagram for diss application.2. implement the previous classes in java. write a main program that can serve as a test class that tests all of the methods created and demonstrates that they are working

For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.