Question 1205405: 1. C ⊃ (D v A) /~C v D
2. A ⊃ H
3. ~H
Found 2 solutions by mccravyedwin, Edwin McCravy:
Answer by mccravyedwin(408)   (Show Source):
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1. C ⊃ (D v A)
2. A ⊃ H
3. ~H /~C v D
| 4. ~(~C v D) Assumption for Indirect Proof
| 5. ~~C • ~D 4, DeMorgan's law
| 6. C • ~D 5, Double Negation
| 7. C 6, Simplification
| 8. D v A 1,7, Modus Ponens
| 9. ~A 2,3, Modus Tollens
|10. A v D 8, Commutation
|11. D 10,9, Disjunctive syllogism
|12. ~D • C 6, Commutation
|13. ~D 12, Simplification
|14. D • ~D 11,13, Conjunction
~C v D lines 4-14 Indirect Proof
Edwin
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
Here is a shorter direct proof. It requires Material Implication
1. C ⊃ (D v A)
2. A ⊃ H
3. ~H /~C v D
4. ~C v (D v A) 1, Material Implication
5. (~C v D) v A 4, Association
6. ~A 2,3, Modus Tollens
7. A v (~C v D) 5, Commutation
8. ~C v D 7,6, Disjunctive Syllogism
Edwin
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