document.write( "Question 588387: I am trying to work on the following proof. I know I used DEM incorrectly on line 3. I cannot figure out what other rule to use. I tried contraposition, but it does not allow me to break down the lines. I cannot use MT or MP without having x or y by itself. I do not know what other conditional rule to use.\r
\n" ); document.write( "\n" ); document.write( "1. X > Y / X . Z > Y
\n" ); document.write( "2. ~X v Y CE 1
\n" ); document.write( "3. ~X . ~Y DEM 3
\n" ); document.write( "4. ~X Simp 3
\n" ); document.write( "5. ~Y Simp 3
\n" ); document.write( "6. X DS 2,5
\n" ); document.write( "7. Y DS 2,4
\n" ); document.write( "8 X v Z Add 6
\n" ); document.write( "9. Z DS 4,8
\n" ); document.write( "10. ~X v Z Conj 4,9
\n" ); document.write( "11. X > Z CE 10
\n" ); document.write( "12. ~Z > ~X Contrap 11
\n" ); document.write( "13. ~Z MT 4,12
\n" ); document.write( "14. ~Z v Y Add 13
\n" ); document.write( "15. Z > Y CE 14
\n" ); document.write( "16. X . Z > Y Conj 6,15\r
\n" ); document.write( "\n" ); document.write( "thank you! \n" ); document.write( "

Algebra.Com's Answer #374479 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Unfortunately you also made a mistake in line 16. Here's one way to derive the conclusion.\r
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document.write( "1.  X > Y             / (X . Z) > Y\r\n" );
document.write( "-------------------------\r\n" );
document.write( "2.  ~X v Y                  1       Material Implication\r\n" );
document.write( "3.  (~X v Y) v ~Z           2       Addition\r\n" );
document.write( "4.  ~X v (Y v ~Z)           3       Association\r\n" );
document.write( "5.  ~X v (~Z v Y)           4       Commutation\r\n" );
document.write( "6.  (~X v ~Z) v Y           5       Association\r\n" );
document.write( "7.  ~(X . Z) v Y            6       De Morgan's Law\r\n" );
document.write( "8.  (X . Z) > Y             7       Material Implication\r\n" );
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