document.write( "Question 1188426: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid: \r
\n" ); document.write( "\n" ); document.write( "A v (~B v ~C), A ⊃ (D ⊃ E), ~(~B v ~D) /.: C ⊃ E \n" ); document.write( "
Algebra.Com's Answer #820410 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "1.  A ∨ (~B ∨ ~C)\r\n" );
document.write( "2.  A ⊃ (D ⊃ E)\r\n" );
document.write( "3.  ~(~B ∨ ~D)     /.: C ⊃ E\r\n" );
document.write( "\r\n" );
document.write( "               |4.  C                 Assumption for conditional proof \r\n" );
document.write( "               |5.  (A ∨ ~B) ∨ ~C     1, Association\r\n" );
document.write( "               |6.  ~C ∨ (A ∨ ~B)     5, Commutation\r\n" );
document.write( "               |7.  ~~C               4, Double negation\r\n" );
document.write( "               |8.  A ∨ ~B            6,7  Disjunctive syllogism   \r\n" );
document.write( "               |9.  ~~B • ~~D         3, deMorgan's law\r\n" );
document.write( "               |10. B • D             1, Double negation\r\n" );
document.write( "               |11. B                 10, Simplification\r\n" );
document.write( "               |12. ~~B               11, Double negation\r\n" );
document.write( "               |13. ~B ∨ A            8, Commutation\r\n" );
document.write( "               |14. A                 13,12, Disjunctive syllogism\r\n" );
document.write( "               |15, D • B             10, Commutation\r\n" );
document.write( "               |16. D                 17, Simplification\r\n" );
document.write( "               |17. (A • D) ⊃ E       2, Importation\r\n" );
document.write( "               |18. A • D             14,15, Conjunction\r\n" );
document.write( "               |19. E                 17,18, Modus ponens\r\n" );
document.write( "20. C ⊃ E      lines 4-19    Conditional proof  \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );