SOLUTION: Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe): 1. ~M U S 2. ~M 3. (M v H) v ~S

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Question 1116635: Write out the conclusion that follows in a single step from the given premises (please read U as horseshoe):
1. ~M U S
2. ~M
3. (M v H) v ~S
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
4.  H           2,1,3 Resolution

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).

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.