The only way that bookstores can profitably sell books at below-market prices is to get the books at a discount from ...

mprezzy March 9, 2020

Not CM

Hello. When I was looking for the not CM, I crossed out the CM making it not CM in the original statement. When I watch the video the instructor is looking for the contrapositive to locate the not CM. Is it suppose to be intuitive thinking to look for the not CM in the contrapositive form since it is the opposite in the original statement?

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SamA March 9, 2020

Hello @mprezzy,

Remember that a contrapositive carries the exact same logic as its counterpart. This means that you can use whichever diagram you prefer. There is no correct way to approach it. However, it is best to always write the contrapositive until you are very comfortable with your sufficient and necessary conditions. You should be able to recognize when a contrapositive is helpful, but you don't always have to use it. I'll copy my diagrams here:

PSBM - -> DP - -> HSV - -> CM or EA
(we were given 'not CM' which I would have crossed out just like you did.)

contrapositive:
not CM and not EA - -> no HSV - -> no DP - -> no PSBM

In this particular case, it is a bit easier to see the right answer using the contrapositive. This is likely why the instructor in the video took that approach. We are given 'not CM'. Then, answer choice D gives us 'not EA'. What should we expect to happen given those two sufficient conditions? Follow the chain, and you will see that profitably selling books is not possible. This is why D is the correct answer.

You didn't do anything wrong, you were right to include 'not CM' in your original diagram. However, you may have gotten to the answer more quickly if you focused on the contrapositive.