I think ‘implies’ asks whether it’s possible that A causes B to be true. In other words, it is false if there is evidence that A does not cause B.
So:
If A is true and B is false, then the result is false, since A could not cause B to be true.
If A and B are both true, then the result is true, since A could cause B.
If A is false and B is true, then the result is true since A could or could not make B true (but another factor could also be making B true)
If A and B are both false we don’t have any evidence about the relationship between A and B, so the result is true.
I don’t know for sure, though. I’m not a mathematician.
What’s important to note is that there has been a big shift in the goals and techniques of education. This most famously occured with “common core” math in the US. It was a push to teach math in a more intuitive way, one that directly corresponds with what children already know. You can physically add things together by putting more of them together, and then counting them, so they try to teach addition with that analog in mind.
Prior to common core math, there was “new math,” which anyone under 80 years old assumes has always been the standard. New math was a push to teach math in a more understandable way, one that gradually introduced new concepts to ensure children understood how math works. This was satirized by Tom Leher in his song “New Math.” If you look up the song, you’ll see that new math mostly was implemented by teaching students how base-10 positional notation works, and then using that understanding to present addition and subtraction as logical algorithms.
Prior to new math, the focus of math education was much more about getting the right answer, rather than the skills needed for problem solving using math. This allows for a higher breadth of education, as topics can be covered quickly, but each topic is understood in a shallow way.