Hi Mike! Thanks for your great question
You're correct that those two inferences you tried to draw are invalid. It's helpful to think about what exactly the double-not arrow means to see why these inferences are invalid:
M is the same as the combination of the following two conditionals:
K not M, and
M not K.
Taking the two rules you mentioned together, this would just tell us that if M is in, then K is not in but P and R are in. We can't read across the double-not arrow to infer anything about the necessary condition in the rule that if M is in, then P and R are in.
If K is not in, all we know is that M could
be in. And if M is not in, all we know is that K could
be in, but this doesn't prevent P and R from being selected (inferring that P and R couldn't be selected would be a Mistaken Negation). As such, we don't know whether P and R must be in, but they could be in, and it is not necessary for either of them to be out if K is in (as your two inferences would suggest). It is possible for K, P, and R to all be in, because P and R can be in even if M is not in; all M
P and R tells us is that P and R must be in when M is in.
I hope this helps, and let me know if you have any other questions!