Are an A O proposition an exclusive OR relationship?

Question

It seems this way because

1. only one and one alone must be true
2. 1 $\implies$ both cannot be true
3. 1 $\implies$ together cannot be false
4. 1 $\implies$ individually propositions can be false

Truth Table below

A O       A ex-OR O
0 0       0
0 1       1
1 0       1
1 1       0

Please check if my analysis is true. If yes, does any book have this ? Copi and Tidman do not seem to have it. I have truth table for other square of opposition relationships too but wanted to start by asking this question.

Answer 1

See Square of opposition: the relation of contradiction between "All S are P" and "Some S are not P" is an "exclusive" relation.

The two are contradictory and

exactly one member of any contradiction is true and one false: they cannot both be true, and they cannot both be false.