Select the Best Translation into Predicate Logic, Using the Following

question 128

Multiple Choice

select the best translation into predicate logic, using the following translation key:
b: Bhavin
c: Chloe
m: Megha
n: Nietzsche
p: Plato
Ax: x is an altruist
Jx: x is joyful
Px: x is a philosopher
Rx: x is Russian
Tx: x is thoughtful
Bxy: x is a brother of y
Mxy: x mocks y
Rxy: x is richer than y
Sxy: x is smarter than y
-The richest philosopher is smarter than any of Chloe's brothers.

• A) (∃x){Px • (∀y)[(Py • y≠x) ⊃ Rxy] • (∀y)(Byc ⊃ Sxy)}
• B) (∃x)(∀y){[(Px • Py) ⊃ Rxy] • (∀z)(Bzc ⊃ Szx)}
• C) (∀x){(Bxc • (∃y)Syx) ⊃ (∃y){[Py • (∀z)(Pz • z≠y)] ⊃ Ryz}}
• D) (∃x){Bxc • (∀y){Syx ⊃ {Py • (∀z)[(Pz • z≠y) ⊃ Ryz]}}}
• E) (∀x){Bxc ⊃ (∀y){[Py • (∃z)(Rxz • Pz)] ⊃ Syx}}

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