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

Algebra ->  Proofs -> 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      Log On


   

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) About Me  (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.
NumberStatementLine(s) UsedReason
1(L ≡ N) ⊃ C
2(L ≡ N) v (P ⊃ ~E)
3~E ⊃ C
4~C
:.~P
5~(L ≡ N)1,4Modus Tollens
6P ⊃ ~E2,5Disjunctive Syllogism
7~(~E)3,4Modus Tollens
8E7Double Negation
9~P6,8Modus Tollens

Here's a list of rules of inference and replacement