Select the Best Translation into Predicate Logic, Using the Following

question 295

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 smartest Russian mocks Chloe and Bhavin.

• A) (∀x){(Mxc • Mxb • Rx) ⊃ [(∀y)(Ry • x≠y) ⊃ Sxy]}
• B) (∃x){Rx • (∀y)[(Ry • y≠x) ⊃ Sxy] • Mxc • Mxb}
• C) (∀x)(∀y){[(Rx • Ry ⊃ Sxy] ⊃ (Mxc • Mxb)}
• D) (∃x){Rx • (∀y)[Sxy ⊃ (Ry • x≠y)] • Mxc • Mxb}
• E) (∃x)(∀y)[(Rx • Ry • y≠x • Sxy) ⊃ (Mxc • Mxb)]

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