Question Database: Formal Logic
Predicate Logic: Translation
Which of the following are well-formed formulas of the langauge of predicate calculus?
I. Fa ∨ (∃x)(Fx & ~Rab)
II. (∀x)xF ⊃ (~Ga & Rab)
III. ~(∀x)(Rab ∨ ~(Fx & Rxc))
IV. (∀x)(Fx ⊃ Gx) ∨ Rxa
A. All of the above
B. I and III
C. III only
D. None of the above
Answer: B
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Translate the following sentences:
All kittens with whiskers love fish.
Kx - x is a kitten
Fx - x loves fish
Gx - x has whiskers
A. (∀x)(Kx & Wx) ⊃ (∀x)Fx
B. (∀x)(Kx ⊃ (Wx & Fx))
C. (∃x)((Kx & Wx) & Fx)
D. (∀x)((Kx & Wx) ⊃ Fx)
Answer: D
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
No kitten that loves fish has green eyes.
Kx - x is a kitten
Fx - x loves fish
Gx - x has green eyes
A. (∀x)((Kx & Fx) ⊃ Gx)
B. ~(∃x)((Kx & Fx) ⊃ Gx)
C. ~(∃x)((Kx & Fx) & Gx)
D. (∃x)((Kx & Fx) & ~Gx)
Answer: C
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Some workers will get a raise only if some of the managers are generous.
Wx - x is a worker
Mx - x is a manager
Rx - x will get a raise
Gx - x is generous
A. (∃x)((Wx & Rx) ⊃ (Mx & Gx))
B. (∃x)((Mx & Gx) ⊃ (Wx & Rx))
C. (∃x) (Wx & Rx) ⊃ (∃x)(Mx & Gx)
D. (∃x)(Mx & Gx) ⊃ (∃x)(Wx & Rx)
Answer: C
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
If anyone passes the exam, then Jill will.
Px - x will pass the exam
j - Jill
A. (∃x)Px ⊃ (∃x)Pj
B. (∃x)(Px ⊃ Pj)
C. (∀x)Px ⊃ Pj
D. (∃x)Px ⊃ Pj
Answer: D
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
B is consistent with the English sentence being false. Suppose a passes, b fails and Jill fails. Then the English sentence is false: someone has passed, but Jill hasn't. However b (or j) is a witness to the truth of B.
Every student must read a book on the reading list.
Sx - x is a student
Bx - x is a book on the reading list
Rxy - x must read y
A. (∀x)(Sx ⊃ (∃y)(By & Rxy))
B. (∀x)(Sx ⊃ (∃y)(By & Ryx))
C. (∀x)(Sx ⊃ (∀y)(By ⊃ Rxy))
D. (∃x)(Bx & (∀y)(Sy ⊃ Ryx))
Answer: A
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Answer could also be D -- the sentence is ambiguous.
Using this dictionary, translate the following formulas:
Px - x is a person
Sx - x is sad
Kx - x is a kitten
Hxy - x is happier than y
Oxy - x owns y
g – George
t - Tracy
Htg ⊃ Sg
A. Either Tracy is happier than George, or George is sad.
B. If George is sad, then Tracy is happier than he is.
C. If Tracy is happier than George, then George is sad.
D. If George is happier than Tracy, then George is sad.
Answer: C
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Using this dictionary, translate the following formulas:
Px - x is a person
Sx - x is sad
Kx - x is a kitten
Hxy - x is happier than y
Oxy - x owns y
g – George
t - Tracy
(∀x)(Px ⊃ (∃y)(Ky & Oxy))
A. Someone owns every kitten.
B. No one owns a kitten.
C. Everyone owns a kitten.
D. Someone owns a kitten.
Answer: C
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Using this dictionary, translate the following formulas:
Px - x is a person
Sx - x is sad
Kx - x is a kitten
Hxy - x is happier than y
Oxy - x owns y
g – George
t - Tracy
(∀x)(Kx & Otx)
A. Tracy owns every kitten.
B. Everything is a kitten owned by Tracy.
C. Tracy owns a kitten.
D. Everything is a kitten that owns Tracy.
Answer: B
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Using this dictionary, translate the following formulas:
Px - x is a person
Sx - x is sad
Kx - x is a kitten
Hxy - x is happier than y
Oxy - x owns y
g – George
t - Tracy
(∀x)((Px & (∃y)(Ky & Oxy)) ⊃ Hx)
A. Everyone who is happy owns a kitten.
B. Someone owns a happy kitten.
C. Everyone who owns a kitten is happy.
D. Eveyone owns a kitten and is happy.
Answer: C
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Using this dictionary, translate the following formulas:
Px - x is a person
Sx - x is sad
Kx - x is a kitten
Hxy - x is happier than y
Oxy - x owns y
g – George
t - Tracy
(∃x)((Hx & Kx) & (∀y)(Py ⊃ Oxy))
A. Everyone who owns something owns a happy kitten.
B. Every happy kitten is owned by someone.
C. Each person owns a happy kitten.
D. There is a happy kitten that owns everyone.
Answer: D
Topic:
Predicate logic, translation
Course Level:
First year formal logic
Notes:
Using this dictionary, translate the following formulas:
Px - x is a person
Sx - x is sad
Kx - x is a kitten
Hxy - x is happier than y
Oxy - x owns y
g – George
t - Tracy
Sg & (∀x)((Px & ~(∃y)(Ky & Oxy) ⊃ Hgx)
A. George is sad, but he’s happier than anyone that doesn’t own a kitten.
B. George is sad, and anyone that owns a kitten is happier than him.
C. George is sad, and if anyone owns a kitten, everyone is happier than him.
D. George is sad, but he is happier than everyone who owns some kitten.
Answer: A
Topic:
Predicate logic, translation
Course Level:
First year formal logic