You’ve gotten good answers already, but I’ll focus on the words.
If you’ve got two possibilities, and the first possibility *excludes* the second possibility, that makes that possibility “exclusive”.
Likewise, if the second possibility *also* excludes the first possibility, it is also “exclusive”.
When both possibilities exclude the other, they are exclusive to each other, or mutually. Mutually exclusive.
Sometimes it’s not always clear how the words came to be used this way, in particular, “exclusive” is typically used in a way that means something more like “rare” or “desirable”, when what it means is “something that excludes”. An “exclusive club” is one that is tough to get into, it excludes people.
The point is, understanding how the word “exclusive” is actually used in this phrase might help you remember what it means.
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