document.write( "Question 1029579: Complete the following natural deduction proof. Thank you!\r
\n" ); document.write( "\n" ); document.write( "1. (R • J) ⊃ U
\n" ); document.write( "2. ~(~R • ~N)
\n" ); document.write( "3. J \r
\n" ); document.write( "\n" ); document.write( "/ U v N
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Algebra.Com's Answer #644574 by robertb(5830)\"\" \"About 
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1. (R • J) ⊃ U----------------Hypothesis
\n" ); document.write( "2. (J • R) ⊃ U----------------Commutativity
\n" ); document.write( "3. J ⊃ ( R ⊃ U) --------------Exportation
\n" ); document.write( "4. J ---------------------Hypothesis
\n" ); document.write( "5. R ⊃ U --------------------Modus ponens on #3 and #4
\n" ); document.write( "6. ~(~R • ~N) -----------------Hypothesis
\n" ); document.write( "7. R v N ---------------------de Morgan's law and double negation
\n" ); document.write( "8. ~~R v N --------------------double negation
\n" ); document.write( "9. ~R ⊃ N -------------------Material implication
\n" ); document.write( "10. ~N ⊃ R -------------------Contrapositive of #9
\n" ); document.write( "11. ~N ⊃ U ------------------Hypothetical syllogism on #5 and # 10
\n" ); document.write( "12. ~~N v U ------------------Material implication
\n" ); document.write( "13. N v U ---------------------Double negation
\n" ); document.write( "14. U v N --------------------Commutativity
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