Either arithmetic and logic are both necessary or logic and geometry are both necessary. If all knowledge is experiential, then even logic is not necessary. So, not all knowledge is experiential.
-Which of the following is the best translation into PL of this argument?
A) (A • L) $ \lor $ (L • G) E ⊃ ∼L / ∼E
B) N $ \lor $ ∼N E ⊃ L / ∼E
C) (A $ \lor $ L) • (L $ \lor $ G) E ⊃ ∼L / ∼E
D) N $ \lor $ ∼N E ⊃ ∼L / ∼E
E) (A • L) $ \lor $ (L • G) E ⊃ L / ∼E

Question

Quizplus · Accepted Answer

Option A correctly translates the argument into propositional logic (PL). It captures the structure of the argument by stating that either arithmetic and logic are both necessary (A • L) or logic and geometry are both necessary (L • G), and if all knowledge is experiential (E), then logic is not necessary (∼L), leading to the conclusion that not all knowledge is experiential (∼E).

Either Arithmetic and Logic Are Both Necessary or Logic and Geometry