My textbook goes into depth about proof techniques and about how to go about proving theorems. However, the author only really focuses on theorems that are stated in the form "if p, then q." I know that a great many theorems have this logical structure, so it is good to know how to prove them, using direct, contrapositive, and contradiction techniques. However, what if a theorem does not have this "if p, then q" structure? What if it is just stated as a fact, p? How are these types of statements proved in general? We can't use a direct proof, because we don't have a hypothesis, and we can't use contrapositive because it is not in the conditional form. Can we only prove it using definitions and/or contradiction?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Book involving proofs

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