1. **Problem Statement:** We have a universal set $U = \{1, 2, 3, \ldots, 29\}$. Set $A$ consists of odd numbers between 10 and 20. Set $B$ consists of factors of 28. We want to analyze these sets and understand their elements for a Venn diagram. 2. **Find Set $A$:** Odd numbers between 10 and 20 are $11, 13, 15, 17, 19$. So, $A = \{11, 13, 15, 17, 19\}$. 3. **Find Set $B$:** Factors of 28 are numbers that divide 28 exactly. The factors of 28 are $1, 2, 4, 7, 14, 28$. So, $B = \{1, 2, 4, 7, 14, 28\}$. 4. **Find Intersection $A \cap B$:** Elements common to both $A$ and $B$. Check each element of $A$ in $B$: - 11 not in $B$ - 13 not in $B$ - 15 not in $B$ - 17 not in $B$ - 19 not in $B$ So, $A \cap B = \emptyset$. 5. **Find Union $A \cup B$:** All elements in $A$ or $B$. $A \cup B = \{1, 2, 4, 7, 11, 13, 14, 15, 17, 19, 28\}$. 6. **Find Complements:** - $A^c = U - A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, \ldots, 29\} \setminus \{11, 13, 15, 17, 19\}$ - $B^c = U - B = \{3, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29\}$ 7. **Summary for Venn Diagram:** - $A = \{11, 13, 15, 17, 19\}$ - $B = \{1, 2, 4, 7, 14, 28\}$ - $A \cap B = \emptyset$ - $U = \{1, 2, 3, \ldots, 29\}$ Since $A$ and $B$ have no common elements, the Venn diagram will show two disjoint circles inside the universal set rectangle. This completes the analysis.