document.write( "Question 1010296: can i have help with these two proofs?
\n" ); document.write( "1. X >Y
\n" ); document.write( "2. (Y v ~X) > (Y > Z) / ~Z > ~X \n" ); document.write( "

Algebra.Com's Answer #625734 by Edwin McCravy(20055) $\"\"$ $\"About$

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can i have help with these two proofs?
\n" ); document.write( "1. X >Y
\n" ); document.write( "2. (Y v ~X) > (Y > Z) / ~Z > ~X
\n" ); document.write( "

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document.write( "The conclusion is equivalent to ~~X > ~~Z by transposition\r\n" );
document.write( "which is equivalent to X > Y by double negation.\r\n" );
document.write( "We first form a conditional proof for X > Z:\r\n" );
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document.write( "1. X > Y \r\n" );
document.write( "2. (Y v ~X) > (Y > Z)         / X > Z\r\n" );
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document.write( "  |3. X               ACP\r\n" );
document.write( "  |4. Y            1,3 MP\r\n" );
document.write( "  |5. Y v ~X         4 Add\r\n" );
document.write( "  |6. Y > Z        2,5 MP\r\n" );
document.write( "7. X > Z           3-6, CP\r\n" );
document.write( "8. ~Z > ~X           7, Transposition\r\n" );
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document.write( " 1. (A & U) < > ~R \r\n" );
document.write( " 2. ~(~R v ~A)            / ~U\r\n" );
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document.write( " 3. ~~R & ~~A          2, DM\r\n" );
document.write( " 4. R & A              3, DN\r\n" );
document.write( " 5. ~~R < > ~(A & U)   1, TR (transposition)\r\n" );
document.write( " 6. R <> ~(A & U)      5, DN\r\n" );
document.write( " 7. R                  4, Simp.\r\n" );
document.write( " 8. ~(A & U)           6,7, MP\r\n" );
document.write( " 9. ~A v ~U            8, DM\r\n" );
document.write( "10. A                  4, Simp.\r\n" );
document.write( "11. ~~A                10, DN\r\n" );
document.write( "12. ~U                 9,11, DS (disjunctive syllogism)\r\n" );
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document.write( "Edwin

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