For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some educated doctors are not gentle.
A) (∃x) (Dx • Ex)
B) (∃x)[(Dx • Ex) • ∼Gx]
C) (∃x)[(Dx • Ex) ⊃ ∼Gx]
D) (∃x)[(Dx • Ex) • Gx]
E) (∃x) ∼[(Dx • Ex) ⊃ ∼Gx]

Question

Quizplus · Accepted Answer

We can represent "educated doctors" as Dx and "gentle" as Gx. To say that "some educated doctors are not gentle", we need to use both predicates and introduce an existential quantifier. Choice B expresses this as "there exists a doctor x who is educated and not gentle". Choice A only expresses that "there exists a doctor x who is educated and gentle", which does not match the given sentence. Choice C is a conditional statement, which says that "if a doctor is educated and gentle, then they are not gentle", which is not equivalent to "some educated doctors are not gentle". Choice D says that "there exists a doctor x who is educated and gentle", which again does not match the given sentence. Choice E is the negation of choice C, which is not equivalent to the original sentence.

For Each of the Following Sentences, Select the Best Translation