SOLUTION: 1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B ⊃ D 4. D ⊃ E / ~D

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Question 1201683: 1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B ⊃ D 4. D ⊃ E / ~D
Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!

Number Statement Lines Used Reason
1 ~N -> [ (B -> D) -> (N v ~E) ]
2 (B -> E) -> ~N
3 B -> D
4 D -> E
:. ~D
5 B -> E 3,4 Hypothetical Syllogism
6 ~N 2,5 Modus Ponens
7 (B -> D) -> (N v ~E) 1,6 Modus Ponens
8 N v ~E 7,3 Modus Ponens
9 ~E 8,6 Disjunctive Syllogism
10 ~D 4,9 Modus Tollens

I used arrows in place of the horseshoe symbols.

For more information, check out the various rules of inference and rules of replacement as shown in the link below.
https://logiccurriculum.com/2019/02/09/rules-for-proofs/

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