I know that $p\rightarrow q$ can be written as $p$' or $q$. Can an equation like ($p'$ or $q$ or $r$) be written as $((p\rightarrow q)\text{ or }r)$?
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1Yes, you can... See Substitution of logical equivalents – Mauro ALLEGRANZA Nov 25 '19 at 12:21
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Why write "$\rightarrow$" as a symbol, but "or" as a word? Why not use both symbols ($\rightarrow, \vee$) or both words (if, then; or). – GEdgar Nov 25 '19 at 13:16
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Yes, this is allowed. The or operation is associative, so when we have several ors in a row, we are allowed to put brackets wherever we want and write
p' or q or r
(p' or q) or r
(p -> q) or r
Usually, you would want to go the other way, though. Certainly, to me, the top row looks simpler to grok than the bottom row.
Arthur
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