Solutions12 - Chapter 12: Hints and Selected Solutions...

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Chapter 12: Hints and Selected Solutions Section 12.3 (page 327) 12.1 The argument is valid and the proof is a good one. In the following, we repeat the proof, but being explicit about the proof methods being used. x [( Brillig ( x ) Tove ( x )) ( Mimsy ( x ) Gyre ( x ))] y [( Slithy ( y ) Mimsy ( y )) Tove ( y )] xSlithy ( x ) x [ Slithy ( x ) Mimsy ( x )] Proof: By the third premise, we know that something in the domain of discourse is slithy. In order to use Elim , let b be one of these slithy things. By the second premise, everything that is either slithy or mimsy is tove. Hence, by Elim , Intro and Elim , we know that b is a tove. By the first premise, using the same methods, we see that b is mimsy and gyre. Hence b is mimsy, using Elim . Thus, b is both slithy and mimsy, using Intro . Hence, something is both slithy and mimsy, by Intro . 12.4 The argument is valid. We give an informal proof. y
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Solutions12 - Chapter 12: Hints and Selected Solutions...

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