Consider a universal set $U = \{1, 2, \dots, 20\}$. Let $A = \{x \in U \mid x ext{ is a multiple of } 3\}$, $B = \{x \in U \mid x ext{ is a multiple of } 5\}$, and $C = \{x \in U \mid x ext{ is a prime number}\}$. Determine the cardinality of the set $(A \cap B) \setminus C$.