1. G ⊃ H
2. ∼G ⊃ (I ⊃ J)
3. K ⊃ L
4. I $ \lor $ K
5. ∼H
-Which of the following propositions is derivable from the given premises using the rules available through section 3.2 (MP, MT, DS, HS, Add, Conj, Simp, CD)?
A) H $ \lor $ L
B) G $ \lor $ L
C) J $ \lor $ L
D) K $ \lor $ J
E) G $ \lor $ K

Question

Quizplus · Accepted Answer

1. G ⊃ H (Given)
2. ∼G ⊃ (I ⊃ J) (Given)
3. K ⊃ L (Given)
4. I $ \lor $ K (Given)
5. ∼H (Given)
From (1) and (5), we can derive ∼G by Modus Tollens (MT). 
From (2) and ∼G, we can derive I ⊃ J by MT. 
From (4) and I, we can derive K by Disjunctive Syllogism (DS). 
From (3) and K, we can derive L by MP. 
Therefore, we can conclude J $ \lor $ L by Addition (Add) and then applying Disjunctive Syllogism (DS) to (2) and J $ \lor $ L to get L.

1 G ⊃ H 2 ∨ \lor ∨ K 5 ∼H -Which of the Following Propositions Is Derivable from

1 G ⊃ H
2 $\lor$ K
5 ∼H
-Which of the Following Propositions Is Derivable from