disjoint events

events A and B are disjoint if they cannot occur at the same time, $\text{[math]}$

given A,B are disjoint events
$\text{[math]}$

generally, $\text{[math]}$ so $\text{[math]}$ iff $\text{[math]}$

if $\text{[math]}$ and $\text{[math]}$ are disjoint, then $\text{[math]}$

given $\text{[math]}$ are disjoint events, then
$\text{[math]}$

given $\text{[math]}$ are disjoint events such that $\text{[math]}$ then:
$\text{[math]}$