document.write( "Question 1118993: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.\r
\n" ); document.write( "\n" ); document.write( "1. A ⊃ (B ⊃ D)
\n" ); document.write( "2. A ⊃ (C ⊃ F) / A ⊃ [(B ⊃ D) • (C ⊃ F)] \n" ); document.write( "

Algebra.Com's Answer #734426 by math_helper(2461) $\"\"$ $\"About$

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There is this logical equivalence, given in many tables where they include equivalences involving conditionals:\r
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document.write( "1.  A —> (B—>D)\r\n" );
document.write( "2.  A —> (C—>F)\r\n" );
document.write( "3.  (A—>(B—>D)) & (A—>(C—>F))        1,2 Conjunction (CONJ)\r\n" );
document.write( "4.  A —> ((B —> D) & (C —> F))       3 Logical equivalence\r\n" );
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document.write( "1.  A —> (B —> D)            Premise\r\n" );
document.write( "2. A —> (C —> F)             Premise\r\n" );
document.write( "3. :: A                      Conditional Proof assumption\r\n" );
document.write( "4. :: B —> D                 3,1 MP\r\n" );
document.write( "5. :: C —> F                 3,2 MP\r\n" );
document.write( "6. :: (B —> D) & (C —> F)    4,5 CONJ\r\n" );
document.write( "7. A—>((B —> D) & (C —> F))  3-6 Conditional Proof\r\n" );
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