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…

Question

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

Accepted Answer

A - 50. |A|=45, |B|=30, |C|=20, |A^B| (mult of 12)=15, |A^C| (36)=5, |B^C| (18)=10, |A^B^C| (36)=5. Exactly one = sum singles - 2*sum pairs + 3*triple = 95 - 60 + 15 = 50.

Answer

B - 40

Answer

C - 48

Answer

D - 44

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…

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