Good analysis, etsevdos, although don't be afraid to be a little less mechanical and a little more holistic in your approach. While conditional diagramming is a useful tool, it is one that is often overused by students who could have gotten there easier and more naturally from a more commonsense approach.
My approach to answer A would be more holistic than diagrammatic. I read it as "if you failed, then you promised" (which leaves out the "oughts" but still captures the essential nature of the claim). My negation would be "failing doesn't mean you promised" or "I can fail at something even if I didn't promise to do it".
Mechanically/diagrammatically, I would probably tackle A this way:
FSOD (Fail at Something you Ought to DO)
PD (Promised to Do it)
The negation of a conditional statement is not simply negating the necessary condition - it's showing that the conditional relationship is, in fact, untrue. So from a purely diagrammatic approach, I would simply take the entire diagram above and cross it out. That, to me, would mean "this is not a true claim". I would NOT negate the necessary condition, like this:
FSOD
PD
Because that means failing proves that you did NOT promise, and that is not the same as saying that failing does NOT prove that you promised. It's too strong, and is the polar opposite when what we want is the logical opposite.
Be more holistic in your approach, and when dealing with conditionals you can negate them by simply saying that the sufficient condition is not, in fact, sufficient to prove the necessary condition. In other words, the sufficient condition can happen EVEN IF the necessary condition does not. The necessary isn't necessary, the sufficient isn't sufficient, the whole thing just isn't true.
I hope that helps. Keep up the good work!
Adam M. Tyson
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