Contrapositive 401
Last add (for a while, anyway) about the contrapositive. If you’ve read the earlier posts (and if you haven’t, you should) on the topic, this should be a review for a short while:
Alex and Bob are two of a group of students, all of whom must take either a math class or an English class. The condition you’re given is, if Alex takes English, the Bob takes math, or, symbolically: A(e) -> B(m). The contrapositive can be diagrammed in the affirmative: If Bob takes English (i.e. “not math”), then Alex takes math (i.e. “not English”): B(e) -> A(m). So:
A(e) ->B(m)
B(e) -> A(m)
That’s the review. Many students mistakenly infer from this that Alex and Bob must be in different classes. But that’s not correct. Notice that there are two conditional relationships – one attaches if Alex takes English, and the other attaches if Bob takes English. There’s nothing there that says they can’t both take math. There will usually be a question or two that will trip you up if you’re not ready for this one. They can’t both be in English, but they could be in math together, or they could be in different classes. Make sure you understand this one; it’s important.
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