Given the following premises:
1)(C • ∼F) ⊃ E
2)G ∨ (C • ∼F)
3)∼(C • ∼F)
A)G ⊃ E 1, 2, HS
B)C 1, Simp
C)C ⊃ (∼F ⊃ E) 1, Exp
D)(G ∨ C) • ∼F 2, Assoc
E)(G ∨ C) • ∼F 2, Assoc.

Question

Quizplus · Accepted Answer

From premise 1 and the simplification of premise 3, we can conclude that C and ∼F both have to be true, since their conjunction is false. Using the rule of conditional transposition, we can rewrite premise 1 as C ⊃ (∼F ⊃ E).

Given the Following Premises