1. Where does the A E I O come from for the four categorical statement types?
These are simply the first four vowels in English. I have been told that A and I come from the Latin “Affirmo” and the E and O from the Latin “Nego,” but I cannot confirm this.
2. If two statements say “Red is my favorite color” and “All my shirts are red” is their relationship independence or implication?
These are logically independent, though practically the connection is easy to see. But what if red was just the favorite color of this guy’s wife?
3. What about “Some students are Canadian” and “Some students are American.” Are these two statement independent as well?
Yes, the truth of one does not impact the truth of the other (assuming that you are not calling Canadians “Americans,” as in citizens of the United States of America).
4. Last question: you mentioned in chapter 13 about four types of relationship between statements as consistency, implication, logical equivalence, independence. Why is inconsistency not included?
I certainly could have included it, but I was just considering inconsistency as the flip side of consistency. Just as two statements can be non-equivalent without naming this as a separate relationship, so two statements can be inconsistent without having to think of this as a separate relationship.