If $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$,and $D = \{15, 17\}$,find $(A \cap B) \cap (B \cup C)$.
First,find the intersection of sets $A$ and $B$:
$(A \cap B) = \{3, 5, 7, 9, 11\} \cap \{7, 9, 11, 13\} = \{7, 9, 11\}$.
Next,find the union of sets $B$ and $C$:
$(B \cup C) = \{7, 9, 11, 13\} \cup \{11, 13, 15\} = \{7, 9, 11, 13, 15\}$.
Finally,find the intersection of the two results:
$(A \cap B) \cap (B \cup C) = \{7, 9, 11\} \cap \{7, 9, 11, 13, 15\} = \{7, 9, 11\}$.
$(A \cap B) = \{3, 5, 7, 9, 11\} \cap \{7, 9, 11, 13\} = \{7, 9, 11\}$.
Next,find the union of sets $B$ and $C$:
$(B \cup C) = \{7, 9, 11, 13\} \cup \{11, 13, 15\} = \{7, 9, 11, 13, 15\}$.
Finally,find the intersection of the two results:
$(A \cap B) \cap (B \cup C) = \{7, 9, 11\} \cap \{7, 9, 11, 13, 15\} = \{7, 9, 11\}$.
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