document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207196>Question 1207196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please use the 18 rules of natural deduction, the 4 instantiation and generalization rules to derive the conclusion of the problem\r<BR>\n" );
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document.write( "1. (x)[Ax ⊃ (Bx ∨ Cx)]<BR>\n" );
document.write( "2. Ag • ~Bg             / Cg  </SPAN>\n" );
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document.write( "I'll discuss how to solve this problem through use of a verbal outline of sorts.<BR>\n" );
document.write( "I'll leave it to the student to construct the formal derivation.\r<BR>\n" );
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document.write( "The (x) out front of premise 1 indicates \"for all x\". <BR>\n" );
document.write( "Sometimes an upside down A is used instead. So the notation would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \forall \text{x}\">\r<BR>\n" );
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document.write( "We use the <font color=red>Universal Instantiation</font> rule to go from <BR>\n" );
document.write( "Ax ⊃ (Bx ∨ Cx)<BR>\n" );
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document.write( "Ag ⊃ (Bg ∨ Cg)<BR>\n" );
document.write( "where g is a specific element.\r<BR>\n" );
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document.write( "For example, x could refer to some country in the set of all countries and g refers to Germany.<BR>\n" );
document.write( "The Universal Instantiation rule is valid because if the rule applies to all elements, then it certainly applies to one specific element of the set.\r<BR>\n" );
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document.write( "Now let's use the <font color=red>simplification</font> rule to break Ag • ~Bg into the separate pieces of Ag and ~Bg\r<BR>\n" );
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document.write( "Next, combine  Ag ⊃ (Bg ∨ Cg) with Ag to apply the <font color=red>Modus Ponens</font> rule.<BR>\n" );
document.write( "This will leave us with Bg ∨ Cg\r<BR>\n" );
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document.write( "Lastly combine Bg ∨ Cg with ~Bg when applying the <font color=red>Disjunctive Syllogism</font> rule. This will let you arrive at Cg.\r<BR>\n" );
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document.write( "Once again this is a verbal outline and I'll leave it to the student to construct the formal derivation.<BR>\n" );
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