Given \( U=\{1,2,3,4,5,6,7,8,9\}, A=\{1,2,3,4\}, B=\{2,4,6\}, C=\{1,3,6,9\} \) Find \( (B \cup C)^{c} \)
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To find \( (B \cup C)^{c} \), we first need to calculate the union of sets \( B \) and \( C \). Given: - \( B = \{2, 4, 6\} \) - \( C = \{1, 3, 6, 9\} \) Now, the union \( B \cup C \) combines all unique elements from both sets: \[ B \cup C = \{2, 4, 6\} \cup \{1, 3, 6, 9\} = \{1, 2, 3, 4, 6, 9\} \] Next, we need to find the complement of \( B \cup C \) in the universal set \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \). The complement \( (B \cup C)^{c} \) consists of all elements in \( U \) that are not in \( B \cup C \). Listing the elements in \( U \) that are not in \( \{1, 2, 3, 4, 6, 9\} \): \[ (B \cup C)^{c} = U - (B \cup C) = \{5, 7, 8\} \] Therefore, the result is: \[ (B \cup C)^{c} = \{5, 7, 8\} \]
