Oh, I just noticed the problem. When you say p(A or B)=1, that assumes that A and B are disjoint, or equivalently that p(A and B)=0.
The theorem you are trying to use when you say p(A or B)=1 is actually:
p(A or B)=p(A)+p(B)-p(A and B)
Ok, this is a definition discrepancy. The or that I’m using is (A or B) <-> not( (not A) and (not B)).
Edit: I was wrong for a different reason.
Oh, I just noticed the problem. When you say p(A or B)=1, that assumes that A and B are disjoint, or equivalently that p(A and B)=0.
The theorem you are trying to use when you say p(A or B)=1 is actually:
p(A or B)=p(A)+p(B)-p(A and B)
Ok, this is a definition discrepancy. The or that I’m using is (A or B) <-> not( (not A) and (not B)).
Edit: I was wrong for a different reason.