Translate into first order logic: 1. “All students are human.” 2. “Some books ar
ID: 3146029 • Letter: T
Question
Translate into first order logic:
1. “All students are human.”
2. “Some books are useful.”
3. “Not all books are useful.”
4. “No dogs are students.”
5. “Every dog has his day.”
6. “Some humans like all dogs.”
7. “Coworkers are humans who have the same (human) boss.”
8. “Tony Stark is Iron Man.”
9. “There is a human who likes all the dogs he has, but no others.”
10. “There is exactly one useful book.”
11. “There is only one dog that likes Tony Stark.”
12. “The tallest dog is taller than the shortest human.”
13. “All dogs are useful.”
14. “Some humans are students.”
15. “Not all humans are students.”
16. “No books are useful.”
17. “Every student has a book.”
18. “There is at least one human who has all books.”
19. “There is a human who has all of the books that he likes.”
20. “Some students have only one dog.”
Given This Knowledge:
Constants:
• IronMan — a hero named Iron Man
• TonyStark — a person named Tony Stark
Functions:
• Height(x) — the height of x
Predicates:
• Book(x) — x is a book
• Day(x) — x is a day
• Dog(x) — x is a dog
• Human(x) — x is a human
Student(x) — x is a student
Useful(x) — x is useful
• Boss(x,y) — x is the boss of y
• Coworker(x,y) — x is a coworker of y
Has(x,y) — x has y
• Likes(x,y) — x likes y
• Equal(x,y) — x and y are the same object
• GT(x,y) — the height x is greater than the height y
Explanation / Answer
(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)
1. “All students are human.”
x (Student(x) -> Human(x))
2. “Some books are useful.”
x (Book(x) ^ Useful(x))
3. “Not all books are useful.”
x (Book(x) ^ ~Useful(x))
4. “No dogs are students.”
x (Dog(x) -> ~Student(x)).
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