Determine and prove whether an argument in English is valid or invalid. Prove whether each argument is valid or invalid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. If the argument is valid, then use the rules of inference to prove that the form is valid. If the argument is invalid, give values for the predicates you defined for a small domain that demonstrate the argument is invalid.
The domain for each problem is the set of students in a class.

Example 1:
Every student on the honor roll received an A.
No student who got a detention received an A.
No student who got a detention is on the honor roll.
Example 1
H(x): x is on the honor roll
A(x): x received an A.
D(x): x got a detention.
∀x (H(x) → A(x))
¬∃x (D(x) ∧ A(x))
∴ ¬∃x (D(x) ∧ H(x))
Valid.
1. ∀x (H(x) → A(x)) Hypothesis
2. c is an arbitrary element Element definition
3. H(c) → A(c) Universal instantiation, 1, 2
4. ¬∃x (D(x) ∧ A(x)) Hypothesis
5. ∀x ¬(D(x) ∧ A(x)) De Morgan's law, 4
6. ¬(D(c) ∧ A(c)) Universal instantiation, 2, 5
7. ¬D(c) ∨ ¬A(c) De Morgan's law, 6
8. ¬A(c) ∨ ¬D(c) Commutative law, 7
9. ¬H(c) ∨ A(c) Conditional identity, 3
10. A(c) ∨ ¬H(c) Commutative law, 9
11. ¬D(c) ∨ ¬H(c) Resolution, 8, 10
12. ¬(D(c) ∧ H(c)) De Morgan's law, 11
13. ∀x ¬(D(x) ∧ H(x)) Universal generalization, 2, 12
14. ¬∃x (D(x) ∧ H(x)) De Morgan's law, 13

Example 2:
No student who got an A missed class.
No student who got a detention received an A.
No student who got a detention missed class.
Example 2
M(x): x missed class
A(x): x received an A.
D(x): x got a detention.
¬∃x (A(x) ∧ M(x))
¬∃x (D(x) ∧ A(x))
∴ ¬∃x (D(x) ∧ M(x))
The argument is not valid. Consider a class that consists of a single student named Frank. If M(Frank) = D(Frank) = T and A(Frank) = F, then the hypotheses are all true and the conclusion is false. In other words, Frank got a detention, missed class, and did not get an A.

Question(c): (confirmed)
Every student who missed class got a detention.
Penelope is a student in the class.
Penelope got a detention.
Penelope missed class.
M(x): x missed class
S(x): x is a student in the class.
D(x): x got a detention.

Question(d): (confirmed)
Every student who missed class got a detention.
Penelope is a student in the class.
Penelope did not miss class.
Penelope did not get a detention.
M(x): x missed class
S(x): x is a student in the class.
D(x): x got a detention.

Question(e)
Every student who missed class or got a detention did not get an A.
Penelope is a student in the class.
Penelope got an A.
Penelope did not get a detention.
M(x): x missed class
S(x): x is a student in the class.
D(x): x got a detention.
A(x): x received an A.

Working on this program in python 3.7: a year in the modern gregorian calendar consists of 365 days. in reality, the earth takes longer to rotate around the sun. to account for the difference in time, every 4 years, a leap year takes place. a leap year is when a year has 366 days: an extra day, february 29th. the requirements for a given year to be a leap year are: 1) the year must be divisible by 42) if the year is a century year (1700, 1800, the year must be evenly divisible by 400some example leap years are 1600, 1712, and 2016.write a program that takes in a year and determines whether that year is a leap year.ex: if the input is 1712, the output is: 1712 is a leap year. ex: if the input is 1913, the output is: 1913 is not a leap year. your program must define and call the function isleapyear(useryear). the function should return true if the input year is a leap year and false otherwise.

Design a class tictactoe that: holds the following information about the game: two-dimensional array (3 by 3), and winner. add additional variables as needed. includes the functions to perform the various operations on objects. for example, function to print the board, getting the move, checking if move is valid, determining if there is a winner after each move. add additional operations as needed. includes constructor(s). write the functions of the class, and write a program that uses the class. the program should declare an object of type tictactoe. the program will create the board and store it in the array. the program will allow two players to play the tic-tac-toe game. after every valid move update the array, check if there is a winner. if there is no winner and no tie, then print the board again to continue.

[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