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
-Exactly three philosophers mock Plato and Nietzsche.
A) (∃x)(∃y)(∃z){Px • Mxp • Mxn • Py • Myp • Myn • Pz • Mzp • Mzn • x≠y • x≠z • y≠z •
(∀w)[(Pw • Mwp • Mwn) ⊃ (w≠x

\lor

w≠y

\lor

w≠z)]}
B) (∃x)(∃y)(∃z){Px • Mxp • Mxn • Py • Myp • Myn • Pz • Mzp • Mzn • x=y • x=z • y=z •
(∀w)[(Pw • Mwp • Mwn) ⊃ (w=x

\lor

w=y

\lor

w=z)]}
C) (∃x)(∃y)(∃z){Px • Mxp • Mxn • Py • Myp • Myn • Pz • Mzp • Mzn • x=y • x=z • y=z •
(∃w)[(Pw • Mwp • Mwn) • (w=x

\lor

w=y

\lor

w=z)]}
D) (∃x)(∃y)(∃z){Px • Mxp • Mxn • Py • Myp • Myn • Pz • Mzp • Mzn • x≠y • x≠z • y≠z •
(∀w)[(Pw • Mwp • Mwn) ⊃ (w=x

\lor

w=y

\lor

w=z)]}
E) (∃x)(∃y)(∃z){Px • Mxp • Mxn • Py • Myp • Myn • Pz • Mzp • Mzn • x≠y • x≠z • y≠z •
(∃w)[(Pw • Mwp • Mwn) • (w≠x

\lor

w≠y

\lor

w≠z)]}

Construct a Model for Each of the Given Theories in the Following

Essay

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