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
-All thoughtful philosophers except Nietzsche are altruists.
A) (∀x)(Px • Tx • x≠n • Ax)
B) (∀x)[x≠n ⊃ (Px • Tx • Ax)]
C) Pn • Tn • ∼An • (∀x)[(Px • Tx • x≠n) ⊃ Ax]
D) (∀x)[(Px • Tx • Ax) ⊃ x≠n]
E) Pn • Tn • ~An • (∀x)[(Px • Tx • Ax) ⊃ x≠n]

Question

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
-All thoughtful philosophers except Nietzsche are altruists.
A) (∀x)(Px • Tx • x≠n • Ax)
B) (∀x)[x≠n ⊃ (Px • Tx • Ax)]
C) Pn • Tn • ∼An • (∀x)[(Px • Tx • x≠n) ⊃ Ax]
D) (∀x)[(Px • Tx • Ax) ⊃ x≠n]
E) Pn • Tn • ~An • (∀x)[(Px • Tx • Ax) ⊃ x≠n]

Quizplus · Accepted Answer

The correct translation is "All thoughtful philosophers except Nietzsche are altruists." This means that if someone is a philosopher and thoughtful, and not Nietzsche, then they are an altruist. Option C correctly captures this logic by stating that Nietzsche is a philosopher and thoughtful but not an altruist, and for all other individuals, if they are philosophers and thoughtful, then they are altruists.

Select the Best Translation into Predicate Logic, Using the Following