document.write( "Question 1171802: use the inference rules, replacement rules, indirect proof and/or conditional proof to derive the conclusion.\r
\n" ); document.write( "\n" ); document.write( "1. F ⊃ ~U
\n" ); document.write( "2. ~F ⊃ P
\n" ); document.write( "3. F v ~F/~U v P
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #797257 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "It's immediate if you can use Constructive Dilemma, which is this:\r\n" );
document.write( "[(p ⊃ q) & (r ⊃ s) & (p v r)] ⊃ (q v s)   \r\n" );
document.write( "\r\n" );
document.write( "But here's how to prove it WITHOUT using Constructive Dilemma.\r\n" );
document.write( "\r\n" );
document.write( " 1. F ⊃ ~U\r\n" );
document.write( " 2. ~F ⊃ P\r\n" );
document.write( " 3. F v ~F  / ~U v P\r\n" );
document.write( "\r\n" );
document.write( "            | 4. ~(~U v P)            Assumption for Indirect Proof\r\n" );
document.write( "            | 5. ~~U & ~P             4, DeMorgan's Law\r\n" );
document.write( "            | 6. U & ~P               5, Double Negation\r\n" );
document.write( "            | 7. U                    6, Simplification \r\n" );
document.write( "            | 8. ~F                   1,7 Modus Tollens\r\n" );
document.write( "            | 9. ~P & U               6, Commutation\r\n" );
document.write( "            |10. ~P                   9, Simplification\r\n" );
document.write( "            |11. ~~F                  2,10 Modus Tollens\r\n" );
document.write( "            |12. F                    11, Double Negation\r\n" );
document.write( "            |13. ~F & ~~F             12,11 Conjunction\r\n" );
document.write( "            |14. ~F & F               13, Double Negation\r\n" );
document.write( "            |15. ~(F v ~F)            14, DeMorgan's Law\r\n" );
document.write( "            |16. (F v ~F) & ~(F v ~F) 3,15 Conjunction\r\n" );
document.write( "17. ~U v P     Lines 4-16    Indirect Proof          \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );