For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-No red flowers are in the garden.
A) ∼(∀x)[(Rx • Fx) ⊃ Gx]
B) (∀x)[(Rx • Fx) ⊃ ∼Gx]
C) (∀x)∼[(Rx • Fx) ⊃ Gx]
D) (∃x)[(Rx • Fx) ⊃ ∼Gx]
E) (∃x)[(Rx • Fx) • ∼Gx]

Question

Quizplus · Accepted Answer

Let R(x) mean "x is red", F(x) mean "x is a flower", and G(x) mean "x is in the garden".
The sentence can be translated as: "For all x, if x is red and x is a flower, then x is not in the garden." This can be represented as (∀x)[(Rx • Fx) ⊃ ∼Gx]. Choice B matches this translation.

For Each of the Following Sentences, Select the Best Translation