Use the Following Key to Determine Which of the Translations $\lor$

use the following key to determine which of the translations of the given English argument to PL is best.
B: Brouwer is an intuitionist.
F: Frege is a logicist.
G: Gödel is a platonist.
H: Hilbert is a formalist.
-It is not the case that either Frege is a logicist or Brouwer is an intuitionist. Gödel being a platonist is necessary and sufficient for Brouwer being an intuitionist. Hilbert is a formalist. So, Gödel is not a platonist; however, Hilbert is a formalist.

A) ∼F $\lor$ B
G ≡ B
H / ∼G • H
B) ∼F $\lor$ B
G ≡ B
H / ∼G ≡ H
C) ∼(F $\lor$ B)
G ≡ B
H / ∼G • H
D) ∼(F $\lor$ B) G ≡ B
H / ∼G ⊃ H
E) ∼(F $\lor$ B) G ≡ B
H / H ⊃ ∼G