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