document.write( "Question 1061555: ~b → ~r
\n" ); document.write( "e → (f → y)
\n" ); document.write( "~(e → y)
\n" ); document.write( "f V (m V r)
\n" ); document.write( "____________
\n" ); document.write( "m V b \n" ); document.write( "

Algebra.Com's Answer #676334 by math_helper(2461) $\"\"$ $\"About$

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I used to be very, very, good at these when I was in my sophomore year of engineering school (1984). I'm trying to re-educate myself in formal logic so I can be helpful. \r
\n" ); document.write( "\n" ); document.write( "& = AND\r
\n" ); document.write( "\n" ); document.write( "—
\n" ); document.write( "1. ~b —> ~r
\n" ); document.write( "2. e —> (f —> y)
\n" ); document.write( "3. ~(e —> y)
\n" ); document.write( "4. f V (m V r)
\n" ); document.write( "—
\n" ); document.write( "// start proof here
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document.write( "5. ~(~e V y)           (3, Impl = material implication)        \r\n" );
document.write( "6. ~~e & ~y           (5, DM= DeMorgan's)\r\n" );
document.write( "7.  ~y                   (6, Simp = Simplification)\r\n" );
document.write( "8.  ~~e                 (6, Simp)\r\n" );
document.write( "9.  e                     (8, DN = double negative)\r\n" );
document.write( "10.  f—>y             (9,2  MP = Modus Ponens)\r\n" );
document.write( "11.  ~f                  (10,7 MT = Modus Tollens, same as contrapositive)\r\n" );
document.write( "12.  m V r             (10,4 MTP = Modus Tollendo Ponens \"affirm by denying\")\r\n" );
document.write( "+13. r                  Conditional (aim is to show if r is true, then b must be true)\r\n" );
document.write( "| 14.  ~~r              (13, DN)\r\n" );
document.write( "| 15. ~~b              (14, 1  MT)\r\n" );
document.write( "| 16.  b                 (15, DN) \r\n" );
document.write( ">14. r—>b           Ends Conditional Proof \r\n" );
document.write( " 15.  m V b            (12,14 Substitution)   Conclusion   \r\n" );
document.write( "—\r\n" );
document.write( "

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