Use the Following Key to Determine Which English Sentence Best $\lor$

use the following key to determine which English sentence best represents the given formula of PL.
A: Peirce studied logic.
B: James was a pluralist.
C: Dewey wrote about thirdness.
D: Dewey denigrated the quest for certainty.
E: Peirce emphasized education.
-∼(C $\lor$ D)

A) It is not the case that Dewey writing about thirdness entails his denigrating the quest for certainty.
B) Dewey did not both write about thirdness and denigrate the quest for certainty.
C) Dewey neither wrote about thirdness nor denigrated the quest for certainty.
D) Either Dewey did not write about thirdness or Dewey did not denigrate the quest for certainty.
E) Dewey not writing about thirdness entails his not denigrating the quest for certainty.