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 ⊃ (A ≡ B)
A) If Dewey wrote about thirdness, then Peirce studied logic just in case James was a pluralist.
B) If Dewey did not write about thirdness, then Peirce studying logic is a necessary condition for James to be a pluralist.
C) Dewey did not write about thirdness provided that Peirce studied logic if, and only if, James was a pluralist.
D) Dewey not writing about thirdness entails Pierce studying logic and James being a pluralist.
E) If Dewey did not write about thirdness, then Peirce studied logic if, and only if, James was a pluralist.

Question

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 ⊃ (A ≡ B)
A) If Dewey wrote about thirdness, then Peirce studied logic just in case James was a pluralist.
B) If Dewey did not write about thirdness, then Peirce studying logic is a necessary condition for James to be a pluralist.
C) Dewey did not write about thirdness provided that Peirce studied logic if, and only if, James was a pluralist.
D) Dewey not writing about thirdness entails Pierce studying logic and James being a pluralist.
E) If Dewey did not write about thirdness, then Peirce studied logic if, and only if, James was a pluralist.

Quizplus · Accepted Answer

The formula can be read as "If C is false, then A is true if and only if B is true." In other words, if Dewey did not write about thirdness (C is false), then Peirce studied logic (A) if and only if James was a pluralist (B). The best choice that represents this formula is option E.

Use the Following Key to Determine Which English Sentence Best