SOB 226 [Typical]



Suppose $X$, $Y$ and $Z$ are sets with $$|X| = 29 \quad |Y| = 20 \quad |Z| = 27,$$
$$|X \cap Y| = 11, \quad |X\cap Z| = 19, \quad |Y \cap Z| = 11,\quad |X \cap Y \cap Z| = 2.$$

Use the inclusion-exclusion principle to calculate $|X \cup Y \cup Z|.$