SOLUTION: Premise: 1. (L ≡ N) ⊃ C 2. (L ≡ N) ∨ (P ⊃ ~E) 3. ~E ⊃ C 4. ~C Conclusion: ~P I need the proof but im struggling

SOLUTION: Premise: 1. (L ≡ N) ⊃ C 2. (L ≡ N) ∨ (P ⊃ ~E) 3. ~E ⊃ C 4. ~C Conclusion: ~P I need the proof but im struggling

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Question 1208773: Premise:
1.
(L ≡ N) ⊃ C
2.
(L ≡ N) ∨ (P ⊃ ~E)
3.
~E ⊃ C
4.
~C
Conclusion:
~P

I need the proof but im struggling
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Premise:
1. (L ≡ N) ⊃ C
2. (L ≡ N) ∨ (P ⊃ ~E)
3. ~E ⊃ C
4. ~C
Conclusion: ~P

Here is one way to do the derivation. There may be other approaches.

Number	Statement	Line(s) Used	Reason
1	(L ≡ N) ⊃ C
2	(L ≡ N) v (P ⊃ ~E)
3	~E ⊃ C
4	~C
:.	~P
5	~(L ≡ N)	1,4	Modus Tollens
6	P ⊃ ~E	2,5	Disjunctive Syllogism
7	~(~E)	3,4	Modus Tollens
8	E	7	Double Negation
9	~P	6,8	Modus Tollens

Here's a list of rules of inference and replacement

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