Lesson 6

Problem. Let \[\begin{align*}A&=\{1, 2, \dotsc, 1000\},\\ B&=\{x \in \mathbb{Z}\colon 1 \le x^{2} \le 200\},\\ C&=\{2, 3, 10\}.\end{align*}\] Find the cardinality of the set \[((A \cap \mathbb{P}) \cup B) \setminus C \ .\]