Set Theoryhard
0:00.0

Let U={xN:1x100}U = \{x \in \mathbb{N} : 1 \le x \le 100\}. Consider the sets A={xU:x is divisible by 2}A = \{x \in U : x \text{ is divisible by } 2\}, B={xU:x is divisible by 3}B = \{x \in U : x \text{ is divisible by } 3\}, and C={xU:x is divisible by 5}C = \{x \in U : x \text{ is divisible by } 5\}. Determine the cardinality of the set D={xU:x is divisible by exactly two of 2,3,5}D = \{x \in U : x \text{ is divisible by exactly two of } 2, 3, 5\}.