Causation doesn't imply correlation and correlation does not imply

causation

Let P := |corr(X,Y) > .5| let Q := exits a relation F: $X\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}Y$

Then the often stated line of correlation does not imply causation is simply! $Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P$.

It is also true that causation does not imply correlation. So! $Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P$

But $(P\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}Q)\vee (Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P)$ is a tautology.

causation

Let P := |corr(X,Y) > .5| let Q := exits a relation F: $X\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}Y$

Then the often stated line of correlation does not imply causation is simply! $Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P$.

It is also true that causation does not imply correlation. So! $Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P$

But $(P\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}Q)\vee (Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P)$ is a tautology.