Question 1193813: Prove using Conditional Proof
1. C ⊃ (D ∨ ∼E)
2. E ⊃ (D ⊃ F) / C ⊃ (E ⊃ F)
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Hints:
When the conclusion is in the form A ⊃ B, and we're doing a conditional proof, we assume that A is the case and try to reach statement B through the rules of inference. That is sufficient to derive the full conclusion of A ⊃ B
If we assume C is the case, then we can get D v ~E through the modus ponens rule (when focusing on premise 1).
That turns into ~E v D and E ⊃ D because of the material implication rule.
We can rewrite premise 2 like so
E ⊃ (D ⊃ F)
(E & D) ⊃ F ... exportation rule
(D & E) ⊃ F
D ⊃ (E ⊃ F) ... exportation rule again
Then notice how we managed to get these two statements
E ⊃ D
D ⊃ (E ⊃ F)
Try to see how you can combine them.
If you need more help, then let me know.
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