document.write( "Question 1116635: Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):\r
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\n" ); document.write( "\n" ); document.write( "3. (M v H) v ~S \n" ); document.write( "
Algebra.Com's Answer #731611 by math_helper(2461)\"\" \"About 
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document.write( "4.  H           2,1,3 Resolution 
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\n" ); document.write( "The rule of Resolution in propositional logic says that if AvB (AvB is true if either A or B is true) and (~AvC) (A is not true or C is true) then one can immediately resolve this to BvC (BvC is true if either B or C is true). This is so because A and ~A appear in two disjunctions involving B and C, respectively. To see why this is, assume A is true. Then the disjunction ~A v C is only true if C is true. If A is not true, then the disjunction A v B is true only if B is true, thus we can conclude, independent of A, BvC (BvC is true if B or C is true).
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\n" ); document.write( "\n" ); document.write( "In the posted problem, 1 says \"not M and S\" while 2 affirms \"not M.\" Since 3 says \"M or H or not S\" we can look at 3 and say, we know \"not M\" (so \"H or not S\" must be true) but 1 refutes \"not S\" so that leaves H as true. \n" ); document.write( "
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