#feedback much prefer the written explanations to the videos :/

I'm so glad! :)

& yes you've got it exactly! /pass --> /study is also the contrapositive of study --> pass and the contrapositive is always logically valid as long as it is derived correctly :)

/brush teeth --> cavities

/cavities --> brush teeth

We can't infer that because brushing his teeth is never on the left side of the diagrams I put above. Brushing his teeth doesn't trigger any of the casual relationships so it's out of the scope of what we know.

We only know what happens if he doesn't brush his teeth or doesn't have cavities. For ex. he could be brushing his teeth for 1 second or not using toothpaste or he could be brushing his teeth and then eating candy right after

We cannot read the arrows both ways, the relationships only function in the direction they point. Hopefully, this all makes sense & helps :)

"Every" was the sufficient condition indicator in the original sentence so I don't think your translation is incorrect, I think 7sage used the same indicator in the negation & as long as the meaning of your symbols is the same, the actual symbols don't need to be identical to what 7sage uses :)