Question 1194113: 55.
1. (L ≡ N) ⊃ C
2. (L ≡ N) v (P ⊃ ~E)
3. ~E ⊃ C
4. ~C /~P
56.
1. ~N ⊃ [(B ⊃ D) ⊃ (N v ~E)]
2. (B ⊃ E) ⊃ ~N
3. B ⊃ D
4. D ⊃ E /~D
5. ~E 1,3, MD
N v ~ E 2,5 Add
57.
1. G ⊃ [~O ⊃ (G ⊃ D)]
2. O v G
3. ~O /D
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Please only post one problem at a time.
I'll do problem 55 to get you started.
| Number | Statement | Line(s) Used | Reason | | 1 | (L = N) -> C | | | | 2 | (L = N) v (P -> ~E) | | | | 3 | ~E -> C | | | | 4 | ~C | | | | :. | ~P | | | | 5 | ~~E | 3, 4 | Modus Tollens | | 6 | ~(L = N) | 1, 4 | Modus Tollens | | 7 | P -> ~E | 2, 6 | Disjunctive Syllogism | | 8 | ~P | 7, 5 | Modus Tollens |
I used a standard equal sign in place of a triple equal sign. 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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