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"
8
$\begingroup$
notation
-
0So that's how you write not-arrow in MathJax! – 2018-03-22
2 Answers
7
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.
-
0Is there a way to formulate $A \nvdash B$ with just and's, or's, and not's? – 2016-09-14
5
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.