document.write( "Question 1141257: (D • E) ∨ F, F → C, (D • E) → ∼B, (∼B ∨ C) → (A → P), ∼P ∴ ∼A \n" ); document.write( "

Algebra.Com's Answer #761908 by Edwin McCravy(20054) $\"\"$ $\"About$

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 1.  (D • E) ∨ F \r\n" );
document.write( " 2.  F → C \r\n" );
document.write( " 3.  (D • E) → ∼B \r\n" );
document.write( " 4.  (∼B ∨ C) → (A → P)\r\n" );
document.write( " 5.  ∼P                      ∴ ∼A\r\n" );
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document.write( " 6. [(~B ∨ C) • A] → P               4, Importation\r\n" );
document.write( " 7. ~[(~B ∨ C) • A]                  6,5, Modus Tollens\r\n" );
document.write( " 8. ~(~B ∨ C) ∨ ~A                   7, deMorgan's law\r\n" );
document.write( " 9. (~~B • ~C) ∨ ~A                  8, deMorgan's law\r\n" );
document.write( "10. (B • ~C) ∨ ~A                    9, Double negation\r\n" );
document.write( "11. ~A ∨ (B • ~C)                   10, commutation\r\n" );
document.write( "12.                  |~~A           Assumption for Indirect Proof\r\n" );
document.write( "13.                  |B • ~C        11,12, Disjunctive syllogism\r\n" );
document.write( "14                   |B             13, Simplification\r\n" );
document.write( "15.                  |~C • B        13, Commutation\r\n" );
document.write( "16.                  |~C            15, Simplification\r\n" );
document.write( "17.                  |~F             2,16 Modus Tollens\r\n" );
document.write( "18.                  |F ∨ (D • E)    1, Commutation\r\n" );
document.write( "19.                  |D • E         18,17, Disjunctive syllogism\r\n" );
document.write( "20.                  |~B             3,19 Modus ponens\r\n" );
document.write( "21.                  |B • ~B        14,20 Conjunction\r\n" );
document.write( "22. ~A                              lines 12-21 indirect proof\r\n" );
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document.write( "Edwin

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