SOLUTION: Use an ordinary proof to show the conclusion can be derived from the premises.
1. ~N ⊃ (~R ⊃ C)
2. R ⊃ N
3. ~C / N
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Proofs
-> SOLUTION: Use an ordinary proof to show the conclusion can be derived from the premises.
1. ~N ⊃ (~R ⊃ C)
2. R ⊃ N
3. ~C / N
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You can put this solution on YOUR website! 1. ~N ⊃ (~R ⊃ C) -------------------Hypothesis
2. (~N &~R) ⊃ C) --------------------exportation
3. ~(N vR) ⊃ C -------------------de Morgan's law
4. ~C ⊃(N vR) -------------------Contrapositive of #3
5. ~C --------------------Hypothesis
6. N v R ---------------------modus ponens on #4 and #5
7. R ⊃ N ---------------------Hypothesis
8. ~R v N ----------------------material implication
9. (N v R) & (N v ~R) ----------------Commutativity on #8, and conjunction on #6 and #8
10. N v ( R & ~R) -------------------distributivity
11. N v F ---------------------negation law
12. N ---------------------Identity Law
