Venn diagram

Each circle holds the outcomes in one event, the lens where circles overlap is the intersection $A \cap B$, and the area outside every circle is the complement of the union. Filling in the overlap first keeps you from double counting, which is the same idea the addition rule enforces with subtraction. In a class of 30 students, 18 play a sport and 12 play an instrument with 7 doing both, so the sport-only region holds $18 - 7 = 11$, the instrument-only region holds $12 - 7 = 5$, and $30 - (11 + 7 + 5) = 7$ students do neither. Mutually exclusive events show up as circles that do not touch.