document.write( "Question 1193812: Prove directly, no Conditional Proof or Indirect Proof\r
\n" ); document.write( "\n" ); document.write( "1. I ∨ (N • F)
\n" ); document.write( "2. I ⊃ F / F \n" ); document.write( "
Algebra.Com's Answer #825892 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "I'll go over the outline of what the derivation would look like.
\n" ); document.write( "This will be an informal paragraph format rather than a formal derivation table, which I'll let you do.\r
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\n" ); document.write( "\n" ); document.write( "The conclusion we want to derive is the statement F
\n" ); document.write( "It's an unfortunate choice of symbol because F is often used to mean \"False\".\r
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\n" ); document.write( "\n" ); document.write( "We can use the distributive rule for premise 1 to go from
\n" ); document.write( "I v (N • F)
\n" ); document.write( "to
\n" ); document.write( "(I v N) • (I v F)
\n" ); document.write( "The first part I v N isn't all that useful
\n" ); document.write( "The second part I v F can be picked out using the simplification rule.\r
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\n" ); document.write( "\n" ); document.write( "Then notice how I v F is the same as ~~I v F and that turns into ~I ⊃ F through the material implication rule.
\n" ); document.write( "Flip things around (transposition rule) to get ~F ⊃ ~~I or ~F ⊃ I\r
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\n" ); document.write( "\n" ); document.write( "We have these statements to focus on
\n" ); document.write( "~F ⊃ I (what we just found)
\n" ); document.write( "I ⊃ F (premise 2)\r
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\n" ); document.write( "\n" ); document.write( "The hypothetical syllogism rule then allows us to combine those two conditionals into ~F ⊃ F
\n" ); document.write( "This turns into ~~F v F or F v F or simply F
\n" ); document.write( "The proof is concluded.
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