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(C) Given sets are $A = \{2, 4, 6, 8, 10, \dots\}$,$B = \{5, 10, 15, 20, \dots\}$,and $C = \{10, 20, 30, \dots\}$.Since $C \subset B$,the union $B \cu

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$C$

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(C) Given sets are $A = \{2, 4, 6, 8, 10, \dots\}$,$B = \{5, 10, 15, 20, \dots\}$,and $C = \{10, 20, 30, \dots\}$.Since $C \subset B$,the union $B \cup C$ is simply $B$.Therefore,$B \cup C = \{5, 10, 15, 20, 25, 30, \dots\} = B$.Now,we find the intersection $A \cap (B \cup C) = A \cap B$.$A \cap B$ represents the set of numbers that are multiples of both $2$ and $5$.The least common multiple of $2$ and $5$ is $10$.Thus,$A \cap B = \{10, 20, 30, \dots\} = C$.

Let $A = \{x : x \in N \text{ and } x \text{ is a multiple of } 2\}$,$B = \{x : x \in N \text{ and } x \text{ is a multiple of } 5\}$,and $C = \{x : x \in N \text{ and } x \text{ is a multiple of } 10\}$. Describe the set $A \cap (B \cup C)$.

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