1. ∼E ⊃ F
2. G • ∼E
-Which of the following propositions is derivable from the given premises using the rules available through section 3.3 (MP, MT, DS, HS, Add, Conj, Simp, CD, DM, Dist, Assoc, Com, DN)?
A) E
B) F
C) ∼G
D) ∼E ⊃ ∼F
E) E $ \lor $ ∼F

Question

Quizplus · Accepted Answer

Given the premises, we can derive F using Modus Ponens (MP). From the first premise, if not E (∼E) then F (∼E ⊃ F), and the second premise states G and not E (G • ∼E). By simplification (Simp), we can derive ∼E from the second premise, and then by applying MP with the first premise, we can derive F.

1 ∼E ⊃ F 2 ∨ \lor ∨ ∼F

1 ∼E ⊃ F
2 $\lor$ ∼F