Either Arithmetic and Logic Are Both Necessary or Logic and Geometry

Multiple Choice

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.
-Consider assuming 'E' for indirect proof of the given argument. Which of the following
Propositions is a likely last line of the indented sequence?

A) (A $\lor$ G) • ∼(A $\lor$ G)
B) E • ∼E
C) L • ∼L
D) All of the above
E) Options B and C, but not option A