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- Using the predicate symbols F(x) for “x is a fruit,” V(x) for “x is a vegetable,” and S(x,y) for “x is sweeter than y,” write wffs that express the following statements. (The domain is the whole world.)a. Some vegetable is sweeter than all fruits.b. Every fruit is sweeter than all vegetables.c. Every fruit is sweeter than some vegetable.d. Only fruits are sweeter than vegetables.Using the predicate symbols S(x) for “x is a student,” I(x) for “x is intelligent,” and M(x) for “x likes music,” write wffs that express the following statements. (The domain is the collection of all people.)a. All students are intelligent.b. Some intelligent students like music.c. Everyone who likes music is a stupid student.d. Only intelligent students like music.Let l(x) be "x has an internet conection" and C(x, y) be "x and y have chatted over the internet". Assume the domain is all students in a class. Express the following using quantifiers. 1. Jerry does not have an internet connection 2. Exactly one student in the class has an internet connection 3. Someone in your class has an internet connection but has not chatted with anyone else in the class.
- A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. Give a logical expression that is equivalent to each English statement. (d) Everyone paid their dues or came on time to the meeting. (e) At least one person paid their dues and came on time to the meeting. (f) There is an officer who did not come on time for the meeting.Answer the following questions about the given statement:∃c : Course • c.private ∧∃co : Customer • (co,c) ∈Books ∧c.name = Customer 4•What does this statement mean?•Is this statement a set or a predicate?•What does the statement evaluate to based on the current system state? Examples for reference:•∃g : Owner • g.name = gymowner ∧g.email = test-There exists an owner with the name gymowner and email test-predicate-false•{c : Course |∃co : Customer • (co,c) ∈Books}-Set of all Courses which are booked by a customer-set-{Boxing,WeightLifting,Yoga1,Wrestling}•{t : Trainer |#{c : Course |(t,c) ∈Teaches}>1}-Set of all Trainers who teach more than 1 class.-set-{Trainer 2}Answer the following questions about the given statement:∃c : Course • c.type = Boxing ∧∃co : Customer • (co,c) ∈Books ∧∃t : Trainer •(t,c) ∈Teaches ∧t.credit >1•What does this statement mean?•Is this statement a set or a predicate?•What does the statement evaluate to based on the current system state? Examples for reference:•∃g : Owner • g.name = gymowner ∧g.email = test-There exists an owner with the name gymowner and email test-predicate-false•{c : Course |∃co : Customer • (co,c) ∈Books}-Set of all Courses which are booked by a customer-set-{Boxing,WeightLifting,Yoga1,Wrestling}•{t : Trainer |#{c : Course |(t,c) ∈Teaches}>1}-Set of all Trainers who teach more than 1 class.-set-{Trainer 2}
- Answer the following questions about the given statement:∀c : Courses • ∃co : Customer • (co,c) ∈Books•What does this statement mean?•Is this statement a set or a predicate?•What does the statement evaluate to based on the current system state? Examples for reference:•∃g : Owner • g.name = gymowner ∧g.email = test-There exists an owner with the name gymowner and email test-predicate-false•{c : Course |∃co : Customer • (co,c) ∈Books}-Set of all Courses which are booked by a customer-set-{Boxing,WeightLifting,Yoga1,Wrestling}•{t : Trainer |#{c : Course |(t,c) ∈Teaches}>1}-Set of all Trainers who teach more than 1 class.-set-{Trainer 2}Answer the following questions about the given statement:{co : Customer |co.classcredit >3 ∧∃c : Course • (co,c) ∈Books ∧¬c.private}•What does this statement mean?•Is this statement a set or a predicate?•What does the statement evaluate to based on the current system state? Examples for reference:•∃g : Owner • g.name = gymowner ∧g.email = test-There exists an owner with the name gymowner and email test-predicate-false•{c : Course |∃co : Customer • (co,c) ∈Books}-Set of all Courses which are booked by a customer-set-{Boxing,WeightLifting,Yoga1,Wrestling}•{t : Trainer |#{c : Course |(t,c) ∈Teaches}>1}-Set of all Trainers who teach more than 1 class.-set-{Trainer 2}Define a predicate int/1 such that ?- int(X). X = 0 ; X = 1 ; X = 2 ; ...
- Consider the following code snippet. 1. /* 2. * The Student class models a student with a name, age 3. * and a faculty in which is currently enrolled in. 4. */ 5. public class Student 6. { 7. // private instance variable, not accessible from outside this class 8. private String firstName; 9. private String lastName; 10. private int birthYear; 11. private String faculty; 12. 13. // The constructor with the. correspondent parameters. 14. public Student(String first, String last, int birthYear, String faculty) 15. { 16. this.firstName= first; 17. this.lastName = last; 18. this.birthYear = birthYear; 19. this.faculty = faculty; 20. } 21. } 1. Implement an accessor method that returns the age of the student given as parameter the current year. 2. Implement a new method called printDetails, taking the currentYear as a parameter, that prints the full name, age and faculty of the student in the following way: Full name: Donald Duck Age: 24 years Faculty:…Please type answers*** Exercise 1.7.8: Determining whether a quantified logical statement is true and translating into English, part 2. infoAbout In the following question, the domain is a set of male patients in a clinical study. Define the following predicates: P(x): x was given the placebo D(x): x was given the medication A(x): x had fainting spells M(x): x had migraines Suppose that there are five patients who participated in the study. The table below shows the names of the patients and the truth value for each patient and each predicate: Name P(x) D(x) A(x) M(x) Frodo T F F T Gandalf F T F F Gimli F T T F Aragorn T F T T Bilbo T T F F For each of the following quantified statements, indicate whether the statement is a proposition. If the statement is a proposition, give its truth value and translate the expression into English. (g) ∃x (D(x) ∧ ¬A(x) ∧ ¬M(x)) (h) ∀x (D(x) → (A(x) ∨ M(x)))Required information Let C(x) be the statement " x has a cat," let D(x) be the statement " x has a dog," and let F(x) be the statement " x has a ferret" Let the domain consist of all students in your class. Express the statement below in terms of C(x),D(x).F(x), quantifiers, and logical connectives. A student in your class has a cat, a dog, and a ferret. Multiple Choice ∀x(C(x)∨D(x)∨P(x)) ∃x(x)∨D(x)∨P(x)) ∀x(C(x)∧D(x)∧P(x)) ∃x(C(x)∧D(x)∧R(x)