So, I see an error. In the Melissa example, the video says that the contrapositive is that "Melissa arrived less than five minutes past the last ring." I think this error confuses opposition and negation.

I think the proper contrapositive would be "Melissa did not arrive more than five minutes past the last ring of the homeroom bell."

Put differently: Melissa arrived five minutes or less past the last ring.

Note that the original argument says "more than five minutes past." It DOES NOT say "five minutes OR more." Big difference, and one that will matter on tricky questions!