document.write( "Question 189540: 3) I can only use the 8 rules of inference...\r
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Algebra.Com's Answer #142225 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In this proof, all we've used is a hypothetical syllogism. This is like saying \"if it rains, then it gets wet outside. If it gets wet outside, then the roads will be slippery. Therefore, if it rains, the roads will be slippery.\". Symbolically, this means that \r
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document.write( "1. (M v N) -> ~S\r\n" );
document.write( "2. T -> (M v N)\r\n" );
document.write( "3. ~S -> ~(M v N) / T -> ~(M v N) \r\n" );
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document.write( "4.  (M v N) -> ~(M v N)              1,3  Hypothetical Syllogism \r\n" );
document.write( "5.  T -> ~(M v N)                    2,4  Hypothetical Syllogism \r\n" );
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