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(a) Show that every propositional formula is equivalent to one using the connectives $\to$ and $\neg$.

(b) Show the same is true for the Sheffer stroke $|$ where $p\mid q$ means "either not $p$ or not $q$" or "not both $p$ and $q$".

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    You can also use `\neg` to obtain $\neg$ and `\to` to obtain $\to$. Choose your favourite.2012-09-18
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    If you are asking here, that strongly suggests you should be checking out some of the standard intro logic textbooks, which will explain this kind of thing in detail. Look up "expressive completeness" or "expressive adequacy" in the index. NB it is always a good move to get a couple of presentations from a couple of different books. Chapter 3 of Teller's *Primer* is freely available at http://tellerprimer.ucdavis.edu/pdf/ and is good. Or there's §11.7 of my *Intro Formal Logic* book. And dozens more of course.2012-09-18

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