Boolean search explained
The counting principle that applies here is inclusion-exclusion.

$$ \left|X \cup Y\right| = \left|X\right| + \left|Y\right| - \left|X \cap Y \right|$$

To make the numbers work out, $\left|X \cap Y \right|$ must be 10000.

A Venn diagram may be more convincing to someone who may be intimidated by the notation.