SOLUTION: Use indirect proof (IP) together with the eight rules of implication and ten rules of replacement to prove that they are valid. Be sure to include the justification for each line,

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Question 1204702: Use indirect proof (IP) together with the eight rules of implication and ten rules of replacement to prove that they are valid. Be sure to include the justification for each line, and offset lines as appropriate for indirect proof.
1. C ⊃ (N • I)
2. (N v P) ⊃ (I ⊃ ~C) /~C
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

The conclusion is ~C
With indirect proofs, or proofs by contradiction, we assume the opposite of the conclusion is the case. Then we show some contradiction arises from this assumption. Thereby proving the original conclusion to be the case.
NumberStatementLine(s) UsedReason
1C --> (N & I)
2(N v P) --> (I --> ~C)
:.~C
3~(~C)Assumption for Indirect Proof
4C3Double Negation
5N & I1, 4Modus Ponens
6I & N5Commutation
7N5Simplification
8I6Simplification
9N v P7Addition
10I --> ~C2, 9Modus Ponens
11~C10, 8Modus Ponens
12C & (~C)4, 11Conjunction
13~C3 - 12Indirect Proof

More info:
Logic Rules of Inference and Replacement

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