Hi,
At the beginning of this video when the instructor is explaining the contrapositives, he says that the contrapositive of doctor --> medical school is no medical school --> not a doctor. But technically for this example, wouldn't not a doctor --> no medical school also make sense? It wouldn't work for the rest of the examples but it would for this one because if one isn't a doctor, they have not gone to medical school and that's why they are not a doctor.
What am I missing in my thinking?
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What you are arguing for is to say that if one is not a doctor, one cannot have gone to medical school. This is not true. One could go to medical school and drop out. One could go to medical school, graduate, and fail the board exam. One could go to medical school, become a doctor, and lose one's license this ceasing to be a doctor. One could go to medical school, be a doctor, and then die, ceasing to be a doctor.
I think there are instances in which what you are thinking is correct: when two things are identical to each other. That is, if we define "champion" as anyone, living or dead, who has won a World Series, and define that anyone who has won a World Series is therefore a champion, we could flip without negating. However this is not the case here.
