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The phrase "are each exclusive" is correct and usable in written English.
It can be used when discussing items or categories that do not overlap or share common elements.
Example: "The two options presented in the proposal are each exclusive, meaning that choosing one will eliminate the possibility of selecting the other."
Alternatives: "are mutually exclusive" or "are individually exclusive".
Exact(1)
The claims are each exclusive of the other and therefore by definition both cannot be true.
Similar(59)
According to Hegel's account of Greek tragedy, the conflict is not between good and evil but between goods that are each making too exclusive a claim.
Intriguingly, type A and type E neurotoxin genes seem to be mutually exclusive and are each restricted to just one of these species.
This "mask war" was vicious because group masks are mutually exclusive; each nullifies the other.
There are at least three different ways a Vice-Presidential pick can go badly; not all are mutually exclusive, and each poses a different sort of risk for Mitt Romney.
The words are mutually exclusive in each of the five folds.
Other scholars have argued that, in the end, the two standards are not exclusive of each other.
We observe that these schemes are not exclusive to each other, since a superposition coding scheme may be reduced to a direct source-to-destination transmission if no band is allocated to the relay-to-destination link.
But those are not exclusive from each other.
The two are intertwined and are not exclusive of each other as they are different sides of the same coin.
These two aren't exclusive of each other, in fact, they're simply the extreme ends of a similar spectrum to the Timmy/Johnny/Spike one above.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com