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

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

Now, suppose that there are dependencies between A, A' and B, B' like below:

A $\displaystyle \rightarrow$ B'

A' $\displaystyle \rightarrow$ B v B' (logical alternative)

B $\displaystyle \rightarrow$ A'

B' $\displaystyle \rightarrow$ 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 $\displaystyle \rightarrow$ B'

B $\displaystyle \rightarrow$ A'

My question:

- how to approach this?

- is this covered in some math topic?

Best Regards,

Greg