SOLUTION: COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF Premises: 1. G ⊃ (E ⊃ N) 2. H ⊃ (~N ⊃ E) Conclusion: G ⊃ ( H ⊃ N)

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Question 1029123: COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF
Premises:
1. G ⊃ (E ⊃ N)
2. H ⊃ (~N ⊃ E)
Conclusion:
G ⊃ ( H ⊃ N)
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
1. G ⊃ (E ⊃ N)--------------Hypothesis
2. (G∧E)⊃N -----------------------Exportation
3. (E∧G)⊃N------------------Commutativity
4. E⊃(G⊃N)------------------Exportation
5. H ⊃ (~N ⊃ E)---------------Hypothesis
6. H⊃(~E⊃N)-----------------Contraposition on part of #5
7. (~E∧H)⊃N------------------Exportation, and the Commutativity
8. ~E⊃(H⊃N)-----------------Exportation
9. ~(H⊃N)⊃E -----------------Contrapositive of #8
10. ~(H⊃N)⊃(G⊃N)----#4 and #9, and hypothetical syllogism
11. (H∧~N)⊃(G⊃N)----Negative of material implication & de Morgan's law
12. H⊃(~N⊃(G⊃N)------Exportation
13. H⊃(~~N∨~G∨N)-----Material implication
14. H⊃(~G∨N)----------- Double negation and N∨N≡ N
15. H⊃(G⊃N)--------------Material implication
16. (H∧G)⊃N---------------Exportation
17. G⊃(H⊃N)---------------Commutativity and exportation
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