Question Database: Formal Logic
Models for Predicate Logic
Eliminating quantifiers
Which of these formulas is a good translation for (∀x)(∃y)Rxy, given a domain D = {a, b}?
A. (Raa & Rab) ∨ (Rba & Rbb)
B. (Raa & Rab) & (Rba & Rbb)
C. (Raa ∨ Rab) & (Rba ∨ Rbb)
D. (Raa ∨ Rab) ∨ (Rba ∨ Rbb)
Answer: C
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
Which of these formulas is a good translation for (∃x)(∀y)Ryx, given a domain D = {a, b}?
A. (Raa & Rab) ∨ (Rba & Rbb)
B. (Raa & Rba) ∨ (Rab & Rbb)
C. (Raa & Rbb) ∨ (Rab & Rba)
D. (Rab & Rbb) ∨ (Rab & Raa)
Answer: B
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
Is the argument from (Raa ∨ Rab) & (Rba ∨ Rbb) to (Raa & Rba) ∨ (Rab & Rbb) valid?
A. Yes, it’s valid.
B. No, it’s not.
Answer: B
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
Is the argument from (∀x)(∃y)Rxy to (∃x)(∀y)Ryx valid?
A. Yes, it’s valid.
B. No, it’s not.
Answer: B
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
Identity
Which of the following statements are true only when more than one thing has property F?
1. Fa & Ga
2. (Fa & Fb) & (Ga & ~Gb)
3. (∃x)Fx & (Ey)Fy
4. (∃x)(∃y)(Fx & Fy)
5. (Fa & Fb) & (~Ga & ~Gb)
A. All of them.
B. None of them.
C. 2 only.
D. 3 and 4 only.
Answer: C
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
5 is consistent with a = b, but 2 is not (since Ga, but ~Gb).
Let a = b be true if and only if the name ‘a’ and the name ‘b’ name the same object.
In a domain D = {c, d, e}, what should we say about the interpretation I(=)?
I(=) |
c |
d |
e |
c |
?? |
||
d |
|||
e |
What valuie should go in the <c, c> slot?
A. 1 (true)
B. 0 (false)
C. can't tell.
Answer: A
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
Let a = b be true if and only if the name ‘a’ and the name ‘b’ name the same object.
In a domain D = {c, d, e}, what should we say about the interpretation I(=)?
I(=) |
c |
d |
e |
c |
1 |
||
d |
?? |
||
e |
What value should go in the <d, c> slot?
A. 1 (true)
B. 0 (false)
C. can't tell.
Answer: B
Topic:
Predicate logic, models
Course Level:
First year formal logic
Notes:
I(=) |
c |
d |
e |
c |
1 |
0 |
0 |
d |
0 |
1 |
0 |
e |
0 |
0 |
1 |