Unformatted text preview: From ¬ V we get ¬ K . But that’s a contradition , because we cannot have both K and ¬ K . What does this mean? Well, it means that H cannot be true, because that assumption led to a contradi-tion which violated the set oF Facts 1-5 we were told about the world. (In particular it led to a contradictory statement that K ∧¬ K . ThereFore we can conclude that ¬ H . Assuming ¬ H , by (1) we get K . By (4’) we get V . By (3’) we get ¬ A . By (2’) we get ¬ R . And the only constraint leFt, (5), is satisfed because ¬ H . This leads us to a solution ( K, ¬ A, ¬ H, ¬ R,V ) which, you can check, does satisFy all the criteria 1-5. It is also a unique solution because we showed two things: ±irst, that H cannot happen. Second, that iF ¬ H then the other Four variables have uniqely assigned values, which are all a consequence oF ¬ H and Facts 1-5. ThereFore this is also the only solution. Page 1 oF 1...
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- Fall '07
- Expression, Vijay, Discrete Mathematic, ¬V