document.write( "Question 1029804: Solve the following proof using natural deduction (rules of replacement and rules of implication).\r
\n" ); document.write( "\n" ); document.write( "1. D v Y
\n" ); document.write( "2. Y ⊃ ~(Z ⊃ D)\r
\n" ); document.write( "\n" ); document.write( "/ Y ≡ ~D\r
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Algebra.Com's Answer #645038 by robertb(5830) $\"\"$ $\"About$

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1. D v Y --------------------Hypothesis
\n" ); document.write( "2. ~~D v Y --------------------double negation
\n" ); document.write( "3. ~D ⊃ Y ---------------------material implication
\n" ); document.write( "4. Y ⊃ ~(Z ⊃ D) ---------------hypothesis
\n" ); document.write( "5. Y ⊃ ~(~Z v D) --------------M.I.
\n" ); document.write( "6. Y ⊃ (Z & ~D) ---------------double neg. and deMorgan's law
\n" ); document.write( "7. ~Yv(Z & ~D) ----------------M.I.
\n" ); document.write( "8. (~Y v Z)&(~Y v ~D)-----------distributivity
\n" ); document.write( "9. ~Y v ~D -------------------simplification
\n" ); document.write( "10. Y ⊃ ~D -------------------M.I.
\n" ); document.write( "11. (~D ⊃ Y)&(Y ⊃ ~D) ---------conjunction on #3 and #10
\n" ); document.write( "12. Y ≡ ~D -------------------- #11 and logical equivalence for ≡ \n" ); document.write( "

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