1. **State the problem:** We have sets \(\xi = \{23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34\}\), \(A = \{\text{even numbers}\}\), \(B = \{23, 29, 31\}\), \(C = \{\text{multiples of 3}\}\), and a set \(D\) with 4 members such that \(D \cap (A \cup C) = \emptyset\). We need to find the members of \(D\). 2. **Identify sets A and C from \(\xi\):** - Even numbers in \(\xi\) (set \(A\)): \(\{24, 26, 28, 30, 32, 34\}\) - Multiples of 3 in \(\xi\) (set \(C\)): \(\{24, 27, 30, 33\}\) 3. **Find \(A \cup C\):** Combine all even numbers and multiples of 3: $$A \cup C = \{24, 26, 27, 28, 30, 32, 33, 34\}$$ 4. **Find the complement \(D\) such that \(D \cap (A \cup C) = \emptyset\):** \(D\) must contain elements of \(\xi\) that are NOT in \(A \cup C\). 5. **List elements of \(\xi\) not in \(A \cup C\):** \(\xi - (A \cup C) = \{23, 25, 29, 31\}\ 6. **Check the size of \(D\):** Set \(D\) has 4 members, and the found elements are \(\{23, 25, 29, 31\}\), which are four. **Final answer:** $$D = \{23, 25, 29, 31\}$$