select the best translation into predicate logic, using the following translation key:
h: Hume
l: Locke
Px: x is a philosopher
Rx: x is a rationalist
Ixy: x influenced y
Sxy: x is more skeptical than y
-If some rationalist is more skeptical than Locke, then no philosopher influenced Hume.
A) (∃x)(Rx • Sxl) ⊃ (∀x)(Px ⊃ ∼Ixh)
B) (∃x)[(Rx • Sxl) ⊃ (∀y)(Py ⊃ ~Iyh)]
C) (∃x)[(Rx • Sxl) ⊃ ~(∃y)(Py ⊃ ~Iyh)]
D) (∃x)(Rx • Sxl) ⊃ ~(∃x)(Px ⊃ ~Ixh)
E) (∃x)[(Rx • Sxl) ⊃ (Px ⊃ ~Ixh)]

Question

Quizplus · Accepted Answer

Option A correctly translates the English sentence into predicate logic. It starts by stating that there exists some rationalist (x) who is more skeptical than Locke (Sxl). The arrow represents an implication, so the consequent states that for all philosophers (x), it is not the case that x influenced Hume. This accurately reflects the statement that if there is a rationalist who is more skeptical than Locke, then no philosopher influenced Hume. The other options either use negations or additional quantifiers that are not necessary in this translation.

Select the Best Translation into Predicate Logic, Using the Following