I'm looking for a way to express A being true does not imply B. I know that A implies B can be written as $A \rightarrow B$, but what about A does not imply B? $A \not\rightarrow B$?
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2Simply write $A\land\neg B$, though that is probably not what you are after. I think you want something like "$p$ is prime does not imply in general that $p$ is odd", right? – Hagen von Eitzen Nov 17 '12 at 17:38
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May be this link help you ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf – Mikasa Nov 17 '12 at 17:40
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@BabakSorouh That tells me how to write the symbol in LaTeX, but not what the symbol means (except possibly by its name). – gerrit Nov 17 '12 at 17:56
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1@HagenvonEitzen Yes, it's the latter I'm after. – gerrit Nov 17 '12 at 17:57
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1I just came here to learn to write $can \nRightarrow should$ – Ben May 02 '17 at 19:50
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So that's how you write not-arrow in MathJax! – A_for_ Abacus Mar 22 '18 at 21:14
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My answer is here: Not necessarily imply – ryang Apr 15 '22 at 19:48
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If you use a generic $\to$ or $\Rightarrow$ for imply then slash through for the not-imply.
But you can perhaps do better. If you actually mean syntactic entailment (so non-implication is a matter of there being no proof from $A$ to $B$ in the relevant proof system) then $A \nvdash B$ is available and absolutely standard.
If you actually mean semantic entailment (so non-implication is a matter of there being a valuation which makes $A$ true without making $B$ true) then $A \nvDash B$ is available and quite standard.
Peter Smith
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1Is there a way to formulate $A \nvdash B$ with just and's, or's, and not's? – Matt Sep 14 '16 at 19:19
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Usually, we use double arrows for implications: $A\Rightarrow B$. You can use a crossed out double arrow for does not imply: $A\nRightarrow B$. In LaTeX, these are "\Rightarrow" and "\nRightarrow", respectively.
icurays1
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2I would usually see single arrow $A \rightarrow B$ and negation $A \nrightarrow B$. – Andrew Wonnacott May 23 '19 at 21:04
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4These are both used. In logic texts, for instance, the object language's notion of implication (i.e., propositional calculus or predicate calculus, etc) is often denoted by $A \to B$, whereas in the meta language (i.e., statements about the object language) the double arrow $A \implies B$ is used. Both are valid but shouldn't be used interchangeably. – Ben Kushigian Nov 01 '19 at 15:05
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2In my opinion, $\implies$ (literally
\impliesin LaTeX) is preferable for communicating logical implication, as $\rightarrow$ is often used to denote functional mappings, etc. – L0tad Jun 08 '23 at 19:36