Final answer:
The Myhill-Nerode theorem is used to determine if a language is regular or not. In this case, the given language (a+b)i(b+c)i is regular because it has only two equivalence classes.
Step-by-step explanation:
A language's regularity can be ascertained using the Myhill-Nerode theorem. The theorem states that a language is not regular if there are an infinite number of equivalency classes in it. There are two potential equivalency classes in the given language (a+b)i(b+c)i: one for strings with an equal number of 'a' and 'b', and another for strings with an equal number of 'b' and 'c'. The language can be considered regular since there are only two possible equivalency classes.
Therefore, the language (a+b)i(b+c)i is regular.