Select the Best Translation into Predicate Logic, Using the Following $\lor$

question 103

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
-Exactly three Russian philosophers are joyful.

• A) (∃x)(∃y)(∃z){Rx • Px • Jx • Ry • Py • Jy • Rz • Pz • Jz • x≠y • x≠z • y≠z •
• (∀w)[(Rw • Pw • Jw) ⊃ (w=x \( \lor \) w=y \( \lor \) w=z)]}
• B) (∃x)(∃y)(∃z){Rx • Px • Jx • Ry • Py • Jy • Rz • Pz • Jz • x≠y • x≠z • y≠z •
• ~(∃w)[Rw • Pw • Jw • (w=x \( \lor \) w=y \( \lor \) w=z)]}
• C) (∃x)(∃y)(∃z){Rx • Px • Jx • Ry • Py • Jy • Rz • Pz • Jz • x≠y • x≠z • y≠z •
• (∃w)[Rw • Pw • Jw • (w=x \( \lor \) w=y \( \lor \) w=z)]}
• D) (∃x)(∃y)(∃z){Rx • Px • Jx • Ry • Py • Jy • Rz • Pz • Jz • x≠y • x≠z • y≠z •
• (∀w)[(Rw • Pw • Jw) ⊃ (w=x • w=y • w=z)]}
• E) (∃x)(∃y)(∃z){Rx • Px • Jx • Ry • Py • Jy • Rz • Pz • Jz • x≠y • x≠z • y≠z •
• (∀w)[(Rw \( \lor \) Pw \( \lor \) Jw) ⊃ (w=x • w=y • w=z)]}

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