19) Define an appropriate language and formalize "There is a student who is loved by every other student" by using FOL formulas.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.3: The Field Of Quotients Of An Integral Domain
Problem 6E
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19) Define an appropriate language and formalize "There is a student who is loved by every other student" by
using FOL formulas.
Jx(Student(x) A Vy · (Student(y) ^ (x = y) → Loves(y, x)))
Jæ ((Student(y) A¬(x = y) → Loves(y, æ)))
Jæ(Student(æ) A Vy · (Student(y) ^¬(x = y) → Loves(y, æ)))
Jæ (Student(x) AVy· (Student(y) → Loves(y, æ)))
Transcribed Image Text:19) Define an appropriate language and formalize "There is a student who is loved by every other student" by using FOL formulas. Jx(Student(x) A Vy · (Student(y) ^ (x = y) → Loves(y, x))) Jæ ((Student(y) A¬(x = y) → Loves(y, æ))) Jæ(Student(æ) A Vy · (Student(y) ^¬(x = y) → Loves(y, æ))) Jæ (Student(x) AVy· (Student(y) → Loves(y, æ)))
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