Suppose you have two sample spaces and . First space contain two outcomes A and A', where A = - A', i.e. the opposite outcomes.
Second space also contains two opposite outcomes B = - B'.
Now, suppose that there are dependencies between A, A' and B, B' like below:
A' B v B' (logical alternative)
B' 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:
- how to approach this?
- is this covered in some math topic?