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]}

Question

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]}

Quizplus · 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.

Select the Best Translation into Predicate Logic, Using the Following