Suppose you have two sample spaces \Omega_A and \Omega_B. First space contain two outcomes A and A', where A = \Omega_A - A', i.e. the opposite outcomes.

Second space also contains two opposite outcomes B = \Omega_B - B'.

Now, suppose that there are dependencies between A, A' and B, B' like below:
A \rightarrow B'
A' \rightarrow B v B' (logical alternative)
B \rightarrow A'
B' \rightarrow A v A' (logical alternative)


So, occurrence of non-negative (i.e. A or B) event excludes such (i.e. non negative) event in the other space. Occurrence of a negative event (A' or B') does not imply anything in the other space. So the two "logical alternative" implications could be in fact skipped:
A \rightarrow B'
B \rightarrow A'


My question:
- how to approach this?
- is this covered in some math topic?

Best Regards,
Greg