Island X (D7)

There are three categories of tribes in Island X; a Truther, who always speaks truthfully; a Liar, who always speaks falsely; and an Altetnator, who makes statements that are alternatively truthful and false, albeit not necessarily in that order.

A visitor approaches three inhabitants and asks who is a Truther. They answer as follows:

A says:
1. I am a Truther
2. B is a Liar

B says:
1. I am a Alternator
2. C is a Liar

C says:
1. I am a Truther
2. A is a Liar

Determine the identity of each of the three inhabitants from the information provided in the above statements.