I was stuck on this for a few minutes, but I think I have figured it out.
Per the rules of the game, the connections we know for sure are:
J----O
M----O
Now, this question is posing that nothing connected to M is also connected to O. If this is true, what does it necessitate? In other words, what would guarantee that nothing is connected to both M and O?
Since J is already connected to O, we know that J cannot be connected to M, eliminating answer choice B.
Further, L----O and L----M do not necessarily stop each other from occurring simultaneously. If L----O, it could still L----M (and vice versa) because the rules allow up to three bridges. Because of this, answer choices D and E are eliminated.
K----O does lock out the possibility of L----O, eliminating the chances of L----O and L----M, which is definitely a step forward; however, it does nothing to eliminate J----M, which would mean that we would have J----O and J----L, violating the sufficient condition in the question. For this reason, answer choice C is out.
If we supposed J----L, this would mean that J----O and J----L are the only options for J (since the rules mandate that J only has two bridges), eliminating the possibility of J----O and J----M.
J must have 2 bridges. It cannot connect to K since K must connect to either O or M for a total of 1 bridge. J also cannot connect with M, since that would be in violation of the sufficient condition in the question. So, the only remaining option is for J----L, and this is necessary to the problem.
