Theory
Example 1
You roll a die. Let be the compound event defined as “more than four dots”, , and be “fewer than three dots”, . That means the intersection between and is the empty set, because they have no outcomes in common. They can never both occur at once.
You denote the empty set with the symbol .
Note! Complementary outcomes are always disjoint, because an event can not both happen and not happen at the same time.