document.write( "Question 1193813: Prove using Conditional Proof\r
\n" ); document.write( "\n" ); document.write( "1. C ⊃ (D ∨ ∼E)
\n" ); document.write( "2. E ⊃ (D ⊃ F) / C ⊃ (E ⊃ F) \n" ); document.write( "
Algebra.Com's Answer #825893 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Hints:\r
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\n" ); document.write( "\n" ); document.write( "When the conclusion is in the form A ⊃ B, and we're doing a conditional proof, we assume that A is the case and try to reach statement B through the rules of inference. That is sufficient to derive the full conclusion of A ⊃ B\r
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\n" ); document.write( "\n" ); document.write( "If we assume C is the case, then we can get D v ~E through the modus ponens rule (when focusing on premise 1).
\n" ); document.write( "That turns into ~E v D and E ⊃ D because of the material implication rule.\r
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\n" ); document.write( "\n" ); document.write( "We can rewrite premise 2 like so
\n" ); document.write( "E ⊃ (D ⊃ F)
\n" ); document.write( "(E & D) ⊃ F ... exportation rule
\n" ); document.write( "(D & E) ⊃ F
\n" ); document.write( "D ⊃ (E ⊃ F) ... exportation rule again\r
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\n" ); document.write( "\n" ); document.write( "Then notice how we managed to get these two statements
\n" ); document.write( "E ⊃ D
\n" ); document.write( "D ⊃ (E ⊃ F)
\n" ); document.write( "Try to see how you can combine them.
\n" ); document.write( "If you need more help, then let me know.
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