When something can be A or B but not both, A and B are mutually exclusive. As sets, A and B would be disjoint.
When everything must be A or B—that is, a thing may be A or B or both, but not neither—what are A and B called? A and B need not be mutually exclusive, but not-A and not-B definitely are.
Here are some examples.
Somebody took cookies from the cookie jar! It could have been Sally or Timmy, but let's not forget that they might be in cahoots; it being Sally or Timmy is [as described above], after all.
If you want to get technical, heads and tails results on a coin are not [as described above], because you missed the very tiny chance that the coin lands on its side.
Clearly, a signed graph cannot at once have a blocknode and two disjoint odd circuits—the two conditions are mutually exclusive. Ideally, they are also [as described above], but as we will show, this is not the case.
To be clear, I'm not looking for mathematical terminology, but something a fluent English speaker could recognize.