select the best translation into predicate logic.
-No apriorist rationalists are skeptics, but Hume is.
A) (∀x)[(Ax • Rx) ⊃ Sx] • Sh
B) (∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh
C) ∼(∀x)[(Ax • Rx) ⊃ Sx] • Sh
D) ∼(∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh

Question

Quizplus · Accepted Answer

- "No apriorist rationalists are skeptics" means that there is no person who is both an apriorist rationalist and a skeptic. This can be translated as:
∀x [(Ax ∧ Rx) → ¬Sx] (for all x, if x is an apriorist rationalist and x is a skeptic, then x is not a skeptic)
- "Hume is a skeptic" can be translated as: Sh (Hume is Sh, where Sh means "x is a skeptic").
- The conjunction of these two statements is: 
∀x [(Ax ∧ Rx) → ¬Sx] ∧ Sh
- Since Hume is the only person mentioned in the sentence, it follows that the second clause (Sh) is equivalent to: 
(∃x)(x=Hume ∧ Sh) (there exists an x such that x is Hume and x is a skeptic)
- Combining the two clauses, we get:
(∀x [(Ax ∧ Rx) → ¬Sx]) ∧ (∃x)(x=Hume ∧ Sh)
- This can be simplified as:
(∀x [(Ax ∧ Rx) → ¬Sx]) ∧ (Sh ∧ Hume)
- Putting it all together, we get:
(∀x [(Ax ∧ Rx) → ¬Sx]) ∧ (Sh ∧ Hume) which is equivalent to (∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh, option B.

Select the Best Translation into Predicate Logic