document.write( "Question 411727: Here is a proof that I have been unable to solve. I can solve it using Indirect Proof but it is listed under the section that states it is solvable by use of the 18 rules of Implication and equivalence. It is driving me nuts!\r
\n" ); document.write( "\n" ); document.write( "Here it is:\r
\n" ); document.write( "\n" ); document.write( "1. (O horseshoe R) horseshoe S
\n" ); document.write( "2. (P horseshoe R) horseshoe ~S /~R\r
\n" ); document.write( "\n" ); document.write( "I know I can derive ~R by Hypothetical Syllogism if I could somehow get rid of the O and the P. I can use exportation to get (O dot R) horseshoe S, and (P dot R)horseshoe ~S, but I can't disconnect those statements from the ones I need to derive a tautology through Material Implication, that is:\r
\n" ); document.write( "\n" ); document.write( "(R horseshoe S)
\n" ); document.write( "(R horseshoe ~S)\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So I'm stuck. This is not an assigned problem; it's one I found. I'm a pretty good beginning logic student and enjoy working all the problems I can find, but this one has me stymied!\r
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Algebra.Com's Answer #289381 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
The ∩ and ∪ are not horseshoes, they are the intersection and union of two sets, respectively. There is some ambiguity here, so I recommend you repost. \n" ); document.write( "

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