Given the universal set \(U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}\), and two subsets \(A = \{1, 2, 3, 4, 5\}\) and \(B = \{5, 6, 7, 8\}\), find the complement of the union of sets A and B.
Answer
Step 2: Find the complement of the union of sets A and B, denoted as \((A \cup B)'\). The complement of a set is the set of elements in the universal set that are not in the given set. So, \((A \cup B)' = U - (A \cup B) = \{9, 10\}\).
Step 1 ：Step 1: Find the union of sets A and B, denoted as \(A \cup B\). The union of two sets is the set of elements which are in A, in B, or in both A and B. So, \(A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8\}\).
Step 2 ：Step 2: Find the complement of the union of sets A and B, denoted as \((A \cup B)'\). The complement of a set is the set of elements in the universal set that are not in the given set. So, \((A \cup B)' = U - (A \cup B) = \{9, 10\}\).
