Questions: Use the Venn diagram to represent the set (A ∪ B)′ in roster form. (A ∪ B)′ = (Use a comma to separate answers as needed.)

Solution Steps

To solve the problem of finding the set \((A \cup B)^{\prime}\) in roster form using a Venn diagram, follow these steps:

1. Understand the Sets: Identify the universal set \(U\) and the subsets \(A\) and \(B\) within it.
2. Union of Sets: Determine the union of sets \(A\) and \(B\), which includes all elements that are in either \(A\) or \(B\).
3. Complement of the Union: Find the complement of the union \((A \cup B)^{\prime}\), which consists of all elements in the universal set \(U\) that are not in \(A \cup B\).
4. Roster Form: List the elements of \((A \cup B)^{\prime}\) in roster form, separated by commas.

We have the universal set \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \), the set \( A = \{2, 4, 6, 8\} \), and the set \( B = \{1, 3, 5, 7, 9\} \).

The union of sets \( A \) and \( B \) is given by: \[ A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \]

The complement of the union \( (A \cup B)^{\prime} \) consists of all elements in the universal set \( U \) that are not in \( A \cup B \): \[ (A \cup B)^{\prime} = U - (A \cup B) = \{10\} \]

The elements of \( (A \cup B)^{\prime} \) in roster form is: \[ (A \cup B)^{\prime} = \{10\} \]

Final Answer