document.write( "Question 1150113: I need help constructing an indirect proof using reductio ad absurdum for:\r
\n" ); document.write( "\n" ); document.write( "~S → (F → L), F → (L → P), therefore, ~S → (F → P)\r
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Algebra.Com's Answer #771628 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1.  ~S → (F → L), \r\n" );
document.write( "2.  F → (L → P),          therefore, ~S → (F → P)\r\n" );
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document.write( "                  | 3. ~[~S → (F → P)]     Assumption for Indirect Proof\r\n" );
document.write( "                  | 4. ~[~S → (~F v P)]    3, Material Implication   \r\n" );
document.write( "                  | 5. ~[~~S v (~F v P)]   4, Material Implication   \r\n" );
document.write( "                  | 6. ~{S v (~F v P)]     5, Double Negation\r\n" );
document.write( "                  | 7. ~S & ~(~F v P)      6, DeMorgan's Law\r\n" );
document.write( "                  | 8. ~S & (~~F & ~P)     7, DeMorgan's Law\r\n" );
document.write( "                  | 9. ~S & (F & ~P)       8, Double Negation  \r\n" );
document.write( "                  |10. ~S                  9, Simplification\r\n" );
document.write( "                  |11. F → L               1,10, Modus Ponens\r\n" );
document.write( "                  |12. (F & ~P) & ~S       9. Commutation\r\n" );
document.write( "                  |13. F & (~P & ~S)       12, Association\r\n" );
document.write( "                  |14. F                   13, Simplification\r\n" );
document.write( "                  |15. L → P               2,14 Modus Ponens\r\n" );
document.write( "                  |16. L                   11,14 Modus Ponens\r\n" );
document.write( "                  |17. P                   15,16 Modus Ponens \r\n" );
document.write( "                  |18. (F & ~P) & ~S       9, Commutation\r\n" );
document.write( "                  |19. (~P & F) & ~S       18, Commutation\r\n" );
document.write( "                  |20. ~P & (F & ~S)       19, Asociation\r\n" );
document.write( "                  |21. ~P                  20, Simplification\r\n" );
document.write( "                  |22. P & ~P              17,21 Conjunction   \r\n" );
document.write( "23.  ~S → (F → P)   Lines 3-22  Indirect Proof\r\n" );
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document.write( "Edwin
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