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.
-If Frege is a logicist and Brouwer is an intuitionist, then Hilbert is a formalist and Gödel is a platonist. Hilbert is not a formalist. Brouwer is an intuitionist. Either Frege is a logicist or both Gödel is not a platonist and Brouwer is an intuitionist. Therefore, Gödel is not a platonist.

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