SOLUTION: 1. C ⊃ (D v A) /~C v D 2. A ⊃ H 3. ~H

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): You can put this solution on YOUR website!

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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