1. **State the problem:** We have three sets: $$\xi = \{23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34\}$$ $$A = \{\text{even numbers in } \xi\}$$ $$B = \{23, 29, 31\}$$ $$C = \{\text{multiples of 3 in } \xi\}$$ We need to find the set \(A' \cap C\), where \(A'\) is the complement of \(A\) relative to \(\xi\). 2. **Find set A:** Even numbers in \(\xi\) are \(24, 26, 28, 30, 32, 34\), so $$A = \{24, 26, 28, 30, 32, 34\}$$ 3. **Find the complement of A \(A'\):** These are elements in \(\xi\) not in \(A\): $$A' = \xi \setminus A = \{23, 25, 27, 29, 31, 33\}$$ 4. **Find set C (multiples of 3 in \(\xi\)):** Multiples of 3 from \(\xi\) are \(24, 27, 30, 33\), so $$C = \{24, 27, 30, 33\}$$ 5. **Find the intersection \(A' \cap C\):** Elements common to both \(A'\) and \(C\): $$A' \cap C = \{27, 33\}$$ **Final answer:** $$\boxed{\{27, 33\}}$$