If the contrapositive is the same as the general statement how can "not both" and "either or" statements have certain posibilities?
In the video it makes sense that there are the two possibilities for each, the general statement and the contrapositive. However, then it introduces a third possibility where with not both you can have not x -> not y and with either or you can have x -> y, but wouldn't the contrapositives of those be the impossibility that the video talks about? I understand the logic behind why they are possibilities, but I do not understand how it works if the contrapositive is supposed to be equivalent to the general statement.
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I'm not sure if I'm quite understanding your question. I actually think that a not both statement is one of the best illustrations of how a contrapositive and the initial statement are the same. If we say that one cannot be both happy and in law school, we know that
If happy then not in law school And If in law school then not happy.
These two statements are contrapositives of each other, mean the same things, and are just two different ways of expressing the idea in the original not both statement.
