document.write( "Question 1029890: Use an ordinary proof to show the conclusion can be derived from the premises.\r
\n" ); document.write( "\n" ); document.write( "1. ~N ⊃ (~R ⊃ C)
\n" ); document.write( "2. R ⊃ N
\n" ); document.write( "3. ~C / N
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Algebra.Com's Answer #644871 by robertb(5830)\"\" \"About 
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1. ~N ⊃ (~R ⊃ C) -------------------Hypothesis
\n" ); document.write( "2. (~N &~R) ⊃ C) --------------------exportation
\n" ); document.write( "3. ~(N vR) ⊃ C -------------------de Morgan's law
\n" ); document.write( "4. ~C ⊃(N vR) -------------------Contrapositive of #3
\n" ); document.write( "5. ~C --------------------Hypothesis
\n" ); document.write( "6. N v R ---------------------modus ponens on #4 and #5
\n" ); document.write( "7. R ⊃ N ---------------------Hypothesis
\n" ); document.write( "8. ~R v N ----------------------material implication
\n" ); document.write( "9. (N v R) & (N v ~R) ----------------Commutativity on #8, and conjunction on #6 and #8
\n" ); document.write( "10. N v ( R & ~R) -------------------distributivity
\n" ); document.write( "11. N v F ---------------------negation law
\n" ); document.write( "12. N ---------------------Identity Law
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