Question 1

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Hume is more skeptical than Locke.
A) Slh
B) Shl
C) hSl
D) lSh
E) hlS

Accepted Answer

The sentence can be translated as "S(h,l)" because it states that Hume (h) is more skeptical than Locke (l), which means that Hume is a subject that has a greater degree of skepticism than Locke.

Question 2

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Locke influenced Hume, but is not more skeptical than him.
A) Ilh • ∼Slh
B) Ihl • ~Shl
C) Ilh • ~Shl
D) (I • ~S)lh
E) Ilh $ \lor $ Shl

Accepted Answer

A

Question 3

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-No philosopher is more skeptical than Hume.
A) (∀x)(Px ⊃ ∼Sxh)
B) ~(∃x)(Px • Shx)
C) (∀x)~(Px ⊃ Sxh)
D) (∀x)(~Sxh ⊃ Px)
E) (∀x)(Shx ⊃ Px)

Accepted Answer

The statement "No philosopher is more skeptical than Hume" can be translated as "For all philosophers x, if x is a philosopher, then x is not more skeptical than Hume." Using the translation key, this becomes (∀x)(Px ⊃ ∼Sxh). Option A is identical to this translation. Option B says that there is no philosopher who is both a philosopher and more skeptical than Hume, but it doesn't rule out the possibility that there are philosophers who are equally skeptical to Hume. Option C says that for all philosophers, it is not the case that if they are a philosopher, then they are more skeptical than Hume. This allows for the possibility that some philosophers are equally skeptical to Hume. Option D says that for all philosophers who are not less skeptical than Hume, they are philosophers. This could allow for the existence of philosophers who are just as skeptical as Hume. Option E says that if someone is more skeptical than Hume, then they must be a philosopher. This doesn't account for the possibility that some philosophers are equally skeptical to Hume. So, option A is the best choice.

Question 4

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Hume influenced some philosophers more skeptical than Locke.
A) (∀x)[Px ⊃ (Sxl • Ihx)]
B) (∃x)[(Px • Ihx) ⊃ Sxl]
C) (∀x)[(Sxl • Ihx) ⊃ Px]
D) (∃x)[(Px • Slx) ⊃ ~Ihx]
E) (∃x)[(Px • Sxl) • Ihx]

Accepted Answer

The correct translation is "There exists some x such that x is a philosopher and x is more skeptical than Locke, and Hume influenced x." This matches option E, which correctly combines existential quantification (∃x) with the conditions that x is a philosopher (Px), x is more skeptical than Locke (Sxl), and Hume influenced x (Ihx).

Question 5

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-All philosophers are more skeptical than some rationalists.
A) (∀x)[Px ⊃ (∀y)(Ry ⊃ Sxy)]
B) (∀x)[Px ⊃ (∀y)(Sxy ⊃ Ry)]
C) (∀x)[Px • (∃y)(Ry • Sxy)]
D) (∀x)[Px ⊃ (∃y)(Ry • Sxy)]
E) (∃x)[Px • (∃y)(Ry • Sxy)]

Accepted Answer

The correct translation is "For all x, if x is a philosopher, then there exists some y such that y is a rationalist and x is more skeptical than y." This captures the idea that every philosopher is more skeptical than at least one rationalist.

Question 6

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Hume is more skeptical than all rationalist philosophers.
A) (∀x)[Sxh ⊃ (Px • Rx)]
B) (∀x)[(Px • Rx) ⊃ Shx]
C) (∀x)[(Px • Rx) ⊃ Sxh]
D) (∀x)[Shx ⊃ (Px • Rx)]
E) (∀x)[(Px • Rx) ≡ Shx]

Accepted Answer

The correct translation is "For all x, if x is a philosopher and x is a rationalist, then Hume is more skeptical than x." This captures the statement that Hume is more skeptical than all rationalist philosophers.

Question 7

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Hume is not more skeptical than some philosophers.
A) ~(∃x)(Px • Sxh)
B) (∃x)(Px • ∼Shx)
C) ~(∀x)(Px • Shx)
D) (∃x)(Px ⊃ ~Shx)
E) (∃x)(~Shx ⊃ Px)

Accepted Answer

The statement can be translated as "There exists some philosopher who is equally or more skeptical than Hume." This can be represented as (∃x)(Px ∧ Sxh) or, equivalently, (∃x)(Px ∧ ¬Shx). Choice B is the only one that matches this translation.

Question 8

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Some philosophers more skeptical than Hume influenced all philosophers more skeptical
Than Locke.
A) (∃x){(Px • Sxh) • (∀y)[(Py • Syl) ⊃ Ixy]}
B) (∃x){(Px • Sxh) • (∀y)[(Py • Sly) ⊃ Ixy]}
C) (∃x){(Px • Shx) • (∀y)[(Py • Sly) ⊃ Ixy]}
D) (∃x){(Px • Shx) • (∀y)[(Py • Sly) ⊃ Iyx]}
E) (∃x){(Px • Sxh) • (∀y)[(Py • Sly) ⊃ Iyx]}

Accepted Answer

- (∃x){(Px • Sxh) - There exists a philosopher x who is more skeptical than Hume.
- (∀y)[(Py • Syl) ⊃ Ixy]} - For all philosophers y who are more skeptical than Locke, x influenced y. 
Option A correctly translates the given statement with proper use of quantifiers and predicates. Option B is incorrect because it uses "Sly" instead of "Syl", which changes the meaning of the statement. Option C and D wrongly use "Shx" and "Sly" instead of "Sxh" and "Syl", respectively, and Option E has the wrong direction in the influence relation (should be Ixy instead of Iyx).

Question 9

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-Some rationalists influenced some philosophers who were more skeptical than them.
A) (∀x){Px ⊃ (∃y)[(Ry • Syx) • Ixy]}
B) (∃x){Px • (∃y)[(Ry • Sxy) • Ixy]}
C) (∃x){Rx • (∃y)[(Py • Syx) • Ixy]}
D) (∃x){Rx • (∃y)[(Py • Sxy) • Iyx]}
E) (∃x){Rx • (∀y)[(Py • Syx) ⊃ Ixy]}

Accepted Answer

The correct translation is "Some rationalists (Rx) influenced (∃y)[Ixy] some philosophers (Py) who were more skeptical than them (Syx)." This captures the essence of the statement by indicating that there exists at least one rationalist who influenced at least one philosopher, and this philosopher was more skeptical than the rationalist.

Question 10

select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-If some rationalist is more skeptical than Locke, then no philosopher influenced Hume.
A) (∃x)(Rx • Sxl) ⊃ (∀x)(Px ⊃ ∼Ixh)
B) (∃x)[(Rx • Sxl) ⊃ (∀y)(Py ⊃ ~Iyh)]
C) (∃x)[(Rx • Sxl) ⊃ ~(∃y)(Py ⊃ ~Iyh)]
D) (∃x)(Rx • Sxl) ⊃ ~(∃x)(Px ⊃ ~Ixh)
E) (∃x)[(Rx • Sxl) ⊃ (Px ⊃ ~Ixh)]

Accepted Answer

Option A correctly translates the English sentence into predicate logic. It starts by stating that there exists some rationalist (x) who is more skeptical than Locke (Sxl). The arrow represents an implication, so the consequent states that for all philosophers (x), it is not the case that x influenced Hume. This accurately reflects the statement that if there is a rationalist who is more skeptical than Locke, then no philosopher influenced Hume. The other options either use negations or additional quantifiers that are not necessary in this translation.

Question 11

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-Some cheetahs are faster than all lions.
A) (∀x)[Lx ⊃ (∃y)(Cy • Fxy)]
B) (∀x)[Lx ⊃ ~(∀y)(Cy • Fyx)]
C) (∃x)(Cx ⊃ (∀y)(Ly ⊃ Fxy)]
D) (∃x)[Cx • (∀y)(Ly ⊃ Fxy)]
E) (∃x)[Cx • (∀y)(Ly • Fxy)]

Accepted Answer

The correct translation is D) because it states that there exists some cheetah (x) such that for all lions (y), the cheetah (x) is faster than the lion (y). This matches the original statement "Some cheetahs are faster than all lions."

Question 12

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-No tiger is faster than all cheetahs.
A) ∼(∃x)[Tx • (∀y)(Cy ⊃ Fxy)]
B) (∀x)[Tx ⊃ ~(∀y)(Cy • Fxy)]
C) (∀x)[Tx ⊃ ~(∃y)(Cy ⊃ Fxy)]
D) ~(∃x)[Cx • (∃y)(Ty . Fyx)]
E) ~(∃x)[Tx • (∀y)(Fyx ⊃ Cy)]

Accepted Answer

The correct translation of "No tiger is faster than all cheetahs" is "It is not the case that there exists a tiger that is faster than every cheetah," which is accurately represented by option A: ∼(∃x)[Tx • (∀y)(Cy ⊃ Fxy)]. This statement negates the existence of any tiger (Tx) that for all cheetahs (Cy), the tiger is faster than the cheetah (Fxy).

Question 13

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-No lion is faster than some tigers.
A) ~(∃x)[Lx • (∀y)(Ty ⊃ Fyx)]
B) (∀x)[Lx ⊃ (∃y)(Ty • ∼Fxy)]
C) ~(∃x)[Lx • (∃y)(Ty • Fxy)]
D) ~(∃x)(∃y)[(Lx • Ty) • Fxy]
E) (∀x)[Lx ⊃ (∀y)(Ty ⊃ ~Fyx)]

Accepted Answer

To express the statement "No lion is faster than some tigers" in predicate logic, we can use the negation of the existential quantifier and the implication. The sentence says that there are some tigers that are faster than all lions. So, we can translate it as: (∀x)[Lx ⊃ (∃y)(Ty • ∼Fxy)], which is option B.

Question 14

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-Some lions are larger than all cheetahs.
A) (∃x)[Lx • (∀y)(Lxy ⊃ Cy)]
B) (∃x)(∀y)[(Lx • Lxy) ⊃ Cy]
C) (∃x)[Lx • (∀y)(Cy ⊃ Lxy)]
D) (∀x)[Cx ⊃ (∃y)(Ly • Lxy)]
E) (∃x)[Lx ⊃ (∀y)(Cy ⊃ Lxy)]

Accepted Answer

The correct translation is "There exists some x, such that x is a lion and for all y, if y is a cheetah, then x is larger than y." This captures the meaning that some lions are larger than all cheetahs.

Question 15

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-Some tigers and all cheetahs are faster than all lions.
A) (∃x)[Tx • (∀y)(Ly ⊃ Fxy)] • (∀x)[Cx • (∀y)(Lz ⊃ Fxy)]
B) (∃x)(∀y)(∀z){(Fyz • Fxz) ⊃ [(Lz • Tx) • Cy]}
C) (∃x)(∀y)(∀z){[(Lz • Tx) • Cy] ⊃ (Fyz • Fxz)]}
D) (∃x)(∀y){(Tx • Cy) ⊃ (∀z)[Lz ⊃ (Fzx • Fzy)]}
E) (∀x){Lx ⊃ [(∃y)(Ty • Fyx) • (∀z)(Cz ⊃ Fzx)]}

Accepted Answer

The correct translation reflects the statement "Some tigers and all cheetahs are faster than all lions" by first indicating that for any lion (Lx), there exists at least one tiger (Ty) that is faster than the lion (Fyx) and all cheetahs (Cz) are faster than the lion (Fzx). This captures both the "some tigers" and "all cheetahs" parts of the statement in relation to their speed compared to "all lions."

Question 16

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-All lions and tigers are larger than some cheetahs, but not faster than all cheetahs.
A) (∀x)(∀y){(Lx • Ty) ⊃ (∃z)[(Cz • Lxz) • Lyz]} • ~(∀x)(∀y)(∀z)(Fxz • Fyz)
B) ~(∃x){Cx • (∀y)[(Ly $ \lor $ Ty) ⊃ (Fxy • Lyx)]}
C) (∀x){(Lx $ \lor $ Tx) ⊃ ~(∃y)[Cy • (Fyx • Lxy)]}
D) (∃x){Cx ⊃ (∀y)(∀z)[(Ly . Tz) ⊃ (~Fxy . ~Lzx)]}
E) (∀x){(Lx $ \lor $ Tx) ⊃ [(∃y)(Cy • Lxy) • ∼(∀y)(Cy ⊃ Fxy)]}

Accepted Answer

The correct translation reflects that all lions and tigers (Lx $ \lor $ Tx) are larger than some cheetahs (∃y)(Cy • Lxy) and not faster than all cheetahs (∼(∀y)(Cy ⊃ Fxy)). This captures the essence of the statement accurately by using existential quantifiers to indicate "some" and negating a universal quantifier to indicate "not all."

Question 17

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-Some cheetahs that are not larger than any lion are faster than some tigers.
A) (∃x){[Cx • (∀y)(Ty ⊃ ~Lxy)] • (∃y)(Ly • Fxy)}
B) (∃x){[Cx • (∀y)(Cy • ~Lxy)] ⊃ (∃y)(Ty • Fxy)}
C) (∃x){Cx • (∀y)(∃z)[(Ly • Tx) • (~Lxy • Fxy)]}
D) (∃x){[Cx • (∀y)(~Lxy ⊃ Lx)] • (∃y)(Fxy • Tx)}
E) (∃x){[Cx • (∀y)(Ly ⊃ ∼Lxy)] • (∃y)(Ty • Fxy)}

Accepted Answer

The correct translation is E) because it accurately represents the statement "Some cheetahs that are not larger than any lion are faster than some tigers." This is broken down as follows: "∃x" indicates there exists some cheetah (Cx), "∀y)(Ly ⊃ ∼Lxy)" means for all y, if y is a lion, then x is not larger than y, and "∃y)(Ty • Fxy)" means there exists some y, such that y is a tiger and x is faster than y. This structure captures the essence of the original statement accurately.

Question 18

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-Any lion larger than all cheetahs is not faster than any tiger.
A) (∀x){[Lx ⊃ (∀y)(Lxy ⊃ Cx)] ⊃ ~(∃y)(Ty • Fxy)}
B) (∀x){Tx ⊃ ~(∃y)[(Ly • Lxy) • (∀z)(Cz ⊃ Fxz)]}
C) (∀x){[Lx • (∀y)(Cx ⊃ Lxy)] ⊃ ∼(∃y)(Ty • Fxy)}
D) (∀x){[Lx ⊃ (∀y)(Cy ⊃ Lxy)] ⊃ (∀y)(Ty ⊃ ~Fxy)}
E) (∀x){[Lx • (∀y)(Cx • Lyx)] ⊃ ~(∃y)(Ty ⊃ ~Fxy)}

Accepted Answer

The sentence starts with "any lion larger than all cheetahs." This can be translated as ∀x[Lx ∧ (∀y)(Cy → Lxy)]. The sentence then says this lion "is not faster than any tiger." This can be translated as ¬(∃y)(Ty ∧ Fxy). Combining these two parts results in (∀x)[Lx ∧ (∀y)(Cx → Lxy)] → ¬(∃y)(Ty ∧ Fxy). Therefore, option C is the best translation.

Question 19

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-No cheetahs that are larger than some tiger are faster than all lions or tigers.
A) ~(∃x){[Cx • (∃y)(Ty • Lxy)] • (∀y)[(Ly • Ty) ⊃ Fxy]}
B) ~(∃x){[Cx • (∃y)(Ty • Fxy)] • (∀y)[(Ly • Ty) ⊃ Lxy]}
C) (∀x){[Cx • (∃y)(Ty • Lxy)] ⊃ ∼(∀y)[(Ly $ \lor $ Ty) ⊃ Fxy]}
D) ~(∃x){[Cx ⊃ (∃y)(Ty • Lxy)] • (∀y)((Ly $ \lor $ Ty) ⊃ Fxy]}
E) ~(∃x){[Cx • (∃y)(Ty • Lxy)] ⊃ ~(∀y)(Ly $ \lor $ Ty) ⊃ Fxy]}

Accepted Answer

The correct translation involves stating that for all x, if x is a cheetah and there exists some y such that y is a tiger and x is larger than y, then it is not the case that for all y, if y is either a lion or a tiger, then x is faster than y. This captures the essence of the statement by using universal quantification to express the generality of the claim and conditional and negation to accurately reflect the relationships and restrictions described.

Question 20

select the best translation into predicate logic, using the following translation key: 
Cx: x is a cheetah
Lx: x is a lion 
Tx: x is a tiger
Fxy: x is faster than y 
Lxy: x is larger than y
-Some lion is faster than all tigers if, and only if, some cheetah is larger than any tiger faster than it.
A) (∃x)[Lx • (∀y)(Ty ⊃ Fxy)] ≡ (∃x){Cx • (∀y)[(Ty • Fyx) ⊃ Lxy]}
B) (∃x)[Lx • (∀y)(Fxy ⊃ Ty)] ≡ (∃x){Cx • (∀y)[Lxy ⊃ (Ty • Fyx)]}
C) (∃x)(∃y)(∀z){[(Lx • Cy) • Tz] • [Fxz ≡ (Fzy ⊃ Lyz)]}
D) (∃x)(∃y)(∀z){[(Lx • Cy) • Tz] • [Fxz ≡ (Lyz ⊃ Fzy)]}
E) (∃x)(∃y)(∀z){[Tz ⊃ (Lx • Cy)] ≡ [(Fxz • Lyz) • Fzy]}

Accepted Answer

- The statement begins with "Some lion is faster than all tigers", which can be translated as (∃x)[Lx • (∀y)(Ty ⊃ Fxy)] 
- The statement ends with "if, and only if, some cheetah is larger than any tiger faster than it", which can be translated as ≡ (∃x){Cx • (∀y)[(Ty • Fyx) ⊃ Lxy]}
- The use of "if, and only if" indicates that the two parts of the statement are equivalent, which is represented by the biconditional symbol (≡)
- Choice B is incorrect because it translates to "Some lion is larger than all animals faster than it", which is not equivalent to the original statement. 
- Choice C is incorrect because it includes unnecessary variables z and does not capture the "if, and only if" relationship between the two parts of the statement. 
- Choice D is incorrect because the direction of the implication is reversed, meaning that it translates to "Some lion is faster than some cheetah who is larger than all tigers faster than it", which is not equivalent to the original statement. 
- Choice E is incorrect because it includes unnecessary variables z and does not capture the "if, and only if" relationship between the two parts of the statement.

Quiz 5: Full First-Order Logic

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Hume is more skeptical than Locke.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Locke influenced Hume, but is not more skeptical than him.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -No philosopher is more skeptical than Hume.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Hume influenced some philosophers more skeptical than Locke.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -All philosophers are more skeptical than some rationalists.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Hume is more skeptical than all rationalist philosophers.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Hume is not more skeptical than some philosophers.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -Some rationalists influenced some philosophers who were more skeptical than them.

select the best translation into predicate logic, using the following translation key: h: Hume l: Locke Px: x is a philosopher Rx: x is a rationalist Ixy: x influenced y Sxy: x is more skeptical than y -If some rationalist is more skeptical than Locke, then no philosopher influenced Hume.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -Some cheetahs are faster than all lions.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -No tiger is faster than all cheetahs.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -No lion is faster than some tigers.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -Some lions are larger than all cheetahs.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -Some tigers and all cheetahs are faster than all lions.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -All lions and tigers are larger than some cheetahs, but not faster than all cheetahs.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -Some cheetahs that are not larger than any lion are faster than some tigers.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -Any lion larger than all cheetahs is not faster than any tiger.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -No cheetahs that are larger than some tiger are faster than all lions or tigers.

select the best translation into predicate logic, using the following translation key: Cx: x is a cheetah Lx: x is a lion Tx: x is a tiger Fxy: x is faster than y Lxy: x is larger than y -Some lion is faster than all tigers if, and only if, some cheetah is larger than any tiger faster than it.