SOLUTION: Use conditional proof: 1. G ⊃ (E ⊃ N) 2. H ⊃ (∼N ⊃ E) / G ⊃ (H ⊃ N)

Question 1169574: Use conditional proof:

1. G ⊃ (E ⊃ N)
2. H ⊃ (∼N ⊃ E) / G ⊃ (H ⊃ N)
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Here's one way to do the derivation. I'm using arrow symbols in place of horseshoe symbols.

The idea is to assume G is the case and show it leads to (H -> N).

Number		Statement	Lines Used	Reason
1		G -> (E -> N)
2		H -> (~N -> E)
:.		G -> (H -> N)
	3	G		Assumption for Conditional Proof
	4	E -> N	1,3	Modus Ponens
	5	(H & ~N) -> E	2	Exportation
	6	(H & ~N) -> N	5,4	Hypothetical Syllogism
	7	H -> (~N -> N)	6	Exportation
	8	H -> (~~N v N)	7	Material Implication
	9	H -> (N v N)	8	Double Negation
	10	H -> N	9	Tautology
11		G -> (H -> N)	3-10	Conditional Proof

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