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Let $$S = \{1, 2, \ldots, 180\}$$. Define $$A$$ as the set of all multiples of 4 in $$S$$, $$B$$ as the set of all multiples of 6 in $$S$$, and $$C$$ as the set of all multiples of 9 in $$S$$. The number of elements in $$S$$ that belong to exactly one of $$A, B, C$$ is
$$|A| = \lfloor 180/4 \rfloor = 45$$, $$|B| = 30$$, $$|C| = 20$$.
$$|A \cap B| = \lfloor 180/12 \rfloor = 15$$, $$|A \cap C| = \lfloor 180/36 \rfloor = 5$$, $$|B \cap C| = \lfloor 180/18 \rfloor = 10$$, $$|A \cap B \cap C| = \lfloor 180/36 \rfloor = 5$$.
Elements in exactly one set $$= \sum |X| - 2 \sum |X \cap Y| + 3|X \cap Y \cap Z|$$
$$= 95 - 2(30) + 3(5) = 95 - 60 + 15 = \mathbf{50}$$.
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