1. **Problem Statement:** Given a Venn diagram with sets A and B containing elements: 3, 6, 15, 2, 10, 5, 7, 11, 13, 17, 20, 16, 8, 4, center 12, and 24 (inside overlap circle), answer the following: 2. **List the elements of A & B:** This means all elements in either set A or set B or both. 3. **List the elements of A \cap B:** This means elements common to both A and B (the overlap). 4. **List the elements of A' \cap B:** This means elements in B but not in A. 5. **List the elements of A \cup B:** This means all elements in A or B or both (same as A & B). --- **Step 1: Identify elements in A and B from the problem statement:** - Elements in A only: 3, 6, 15, 2, 10, 5, 7, 11, 13, 17, 20, 16, 8, 4 - Elements in B only: 24 - Elements in A \cap B (overlap): 12 **Step 2: List elements of A & B (all elements in A or B or both):** $$A \cup B = \{3,6,15,2,10,5,7,11,13,17,20,16,8,4,12,24\}$$ **Step 3: List elements of A \cap B (common elements):** $$A \cap B = \{12\}$$ **Step 4: List elements of A' \cap B (elements in B but not in A):** Since 24 is in B but not in A, $$A' \cap B = \{24\}$$ **Step 5: List elements of A \cup B (all elements in A or B or both):** Same as step 2, $$A \cup B = \{3,6,15,2,10,5,7,11,13,17,20,16,8,4,12,24\}$$ --- **Final answers:** - a. Elements of A & B: $\{3,6,15,2,10,5,7,11,13,17,20,16,8,4,12,24\}$ - b. Elements of $A \cap B$: $\{12\}$ - c. Elements of $A' \cap B$: $\{24\}$ - d. Elements of $A \cup B$: $\{3,6,15,2,10,5,7,11,13,17,20,16,8,4,12,24\}$