if $A_1$ and $A_2$ are two events, then $P(A_1 | A_2) \leq P(A_1) + P(A_2)$. $A_1 \cup A_2$ and $A_1 \vee A_2$ both denote the union of the events $A_1$ and $A_2$, i.e., the event that $A_1$ or $A_2$ holds, or both.) More generally,

$P(A_1 \cup ... \cup A_n) \leq \sum\limits_{i=1}^n P(A_i)$