How To Prove It
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How To Prove It Solution Manual
How to prove it How to prove it Proof by example The author gives only the case n=2 and suggests that it contains mostof the ideas of the general proof.Proof by intimidation 'Trivial'Proof by vigorous handwaving Works well in a classroom or seminar setting.Proof by cumbersome notation Best done with access to at least four alphabets and special symbols.Proof by exhaustion An issue or two of a journal devoted to your proof is useful.Proof by omission 'The reader may easily supply the details.' 'The other 253 cases are analogous.' Proof by obfuscation A long plotless sequence of true and/or meaningless syntactically relatedstatements.Proof by wishful citation The author cites the negation, converse, or generalization of a theoremfrom the literature to support his claim.Proof by funding How could three different government agencies be wrong?Proof by eminent authority 'I saw Karp in the elevator and he said it was probably NP-complete.'
Proof by personal communication 'Eight-dimensional coloured cycle stripping is NP-complete (Karp,personal communication).' Proof by reduction to the wrong problem 'To see that infinite-dimensional coloured cycle stripping isdecidable, we reduce it to the halting problem.' Proof by reference to inaccessible literature The author cites a simple corollary of a theorem to be found in a privatelycirculated memoir of the Slovenian Philological Society, 1883.Proof by importance A large body of useful consequences all follow from the propositionin question.Proof by accumulation of evidence Long and diligent search has not revealed a counterexample.Proof by cosmology The negation of the proposition is unimaginable or meaningless. Popularfor proofs of the existence of God.Proof by mutual reference In reference A, Theorem 5 is said to follow from Theorem 3 in referenceB, which is shown to follow from Corollary 6.2 in reference C, which isan easy consequence of Theorem 5 in reference A.Proof by metaproof A method is given to construct the desired proof. The correctness ofthe method is proved by any of these techniques.Proof by picture A more convincing form of proof by example.
I go back and forth with it. I find the beginning chapters to be kind of a clunky introduction to logic. I appreciate Velleman's attempt to avoid mathematics here, but I don't think real world scenarios (often with several factors and grey areas) are any better suited to convey the subtleties of logic. I think most of the examples could be rewritten to something simpler involving extremely elementary mathematics that just about anyone reading the book would understand.I've never tried learning from the text alone, but it's a pretty standard Intro To Proofs course text, and it's not a bad book by any means.