WE HAVE BEEN COMPUTING IN PSEUDO-EXCLUSION MODE
OR, XOR and NOR are not a true exclusion operations. Now that we have EI (either) we might relegate the X and N operator prefixes to obsolescence.
The designers of the logic in question declared/defined around the necessary term (EI) and created the XOR, NOR and XNOR operators that EI (either) would have handled to begin with.
AND gates handle the inclusion of identical values as true. It's complementary state EI (either) computes the exclusion of all but one, the exception. For two different values the EI (either) operator output will be true.
With AND and EI there exists a simplification of the operator set needed to represent logic gates in circuit design and central processing units.
The two operators AND/EI handle all of the truth table possibilities.
The letter C (inverting buffer) can be used to declare the complementary result as true where a one value is necessary.
The application of this logic is similar to functional programming in that it takes a mutable operator (OR) and replaces it with EI which responds true ONLY when at least one value differs. Whereas OR can be either and both, even in digital electronics the truth is masked as the OR circuit operates like the AND circuit when input values are the same. EI (either) spares the complication of pseudo-exclusion by implementing EXCEPTION though might be a more strict to design style/environment.
In digital logic OR can be more fundamentally expressed as AND * EI = OR, where OR is a superset of the low level AND EI.