Negation vs Mistake in Negation

[tessajw]

I have a question about the difference between a mistake in negation and a negation.
Because if a negation is true, than the original statement would be false.
So how would a mistake in negation work? Wouldnt that just correctly prove the original statement if the negation is false? How can you incorrectly negate something if a negation is incorrect itself?

How does one "correctly negate" as opposed to "making a mistake in negation" ?

[tessajw]

Okay I have an example here. It states that the following is a mistake in negation , but it is quite literally what we were taught to do - reverse and take the contrapositive. How is this a mistake in negation? Or is a mistake in negation = contrapositive

I will just explain it cuz I cant attatch anything. The statement was flawed paralell reasoning and it had a mistake in reversal. This says answer choice b is incorrect because it says:

rule: Discovered something new ---> has examined every solution
fran: Hasnt discovered something new ----> hasnt examined every solution

???? isn't this exactly what we were taught is the correct thing to do? Reverse and contrapositive? How is this a mistake in negation.

[tessajw]

Oh actually totally ignore second one, it wasnt reversed i guess i just cant read.