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? $A \not\rightarrow B$?
Notation for "A does not imply B"
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$\begingroup$
notation
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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? – 2012-11-17
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0May be this link help you ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf – 2012-11-17
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0@BabakSorouh That tells me how to write the symbol in LaTeX, but not what the symbol means (except possibly by its name). – 2012-11-17
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1@HagenvonEitzen Yes, it's the latter I'm after. – 2012-11-17
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1I just came here to learn to write $can \nRightarrow should$ – 2017-05-02
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0So that's how you write not-arrow in MathJax! – 2018-03-22
2 Answers
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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.
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0Is there a way to formulate $A \nvdash B$ with just and's, or's, and not's? – 2016-09-14
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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.