In case of distinct edges, an MST will ALWAYS have the lightest, and the second lightest edge. Complement the circumstances here, and Options A and B become True. Option C is also True
Note that the third lightest edge may or may not be included in the MST, because it might form a loop.
Whenever we have distinct edges, we ALWAYS get a unique MST. Complement the circumstances, and Option E becomes True.
In an MST, the only reason we include a heavier edge, when we have lighter options is when that edge is a bridge (cut edge). We need to include it in order to keep the MST connected.
For similar reason, in a Maximum-Spanning-Tree, if the minimum-weight edge is a bridge, we will include it.
Option D is False, and is our answer.
https://gateoverflow.in/39727/gate2016-1-40