A course in logic is often offered in a Phil Dept, perhaps as a way to meet liberal studies requirements (that's where I took it, and where the course is at the

A course in logic is often offered in a Phil Dept, perhaps as a way to meet liberal studies requirements (that's where I took it, and where the course is at the school where I now teach). The equivalence of A => B and ~B => ~A is taught in every college and university CS program I've ever seen, as part of a standard course that may be called something like Discrete Math. I teach this course out of a book by Rosen and another popular author is Epp. This equivalence is also, as many other posters noted, perfectly natural to a person with a technical bent. But I understood the piece's author's point to be that they are looking for a certain maturity. When we teach, we see that there are stages of competence through which students pass. First they are able to ape the required work on a sentence-by-sentence basis, but not whole problems from start to finish. Next they are able to reliably work entire problems, but only in a context (for instance, they can do induction in the Induction section but outside of it they are easily confused). Finally, with enough practice, they have a larger view and can select the appropriate tool for the job when there are a lot of tools lying around, as well as apply that tool. (FWIW, I take the posters here saying that the author didn't prompt well enough to be recognizing those stages, implicitly.)