1. **State the problem:** We are given two sets $A$ and $B$ which are subsets of the universal set $S = \{1,2,3,\ldots,20\}$. We need to find the union $A \cup B$ and the intersection $A \cap B$. 2. **Recall definitions:** - The union $A \cup B$ is the set of all elements that are in $A$, or in $B$, or in both. - The intersection $A \cap B$ is the set of all elements that are in both $A$ and $B$. 3. **Given sets:** $$ A = \{1,2,5,6,7,8,10,11,13,14,15\} $$ $$ B = \{4,6,7,8,9,10,13,14,15,16,18,19\} $$ 4. **Find $A \cup B$:** Combine all unique elements from both sets: $$ A \cup B = \{1,2,4,5,6,7,8,9,10,11,13,14,15,16,18,19\} $$ 5. **Find $A \cap B$:** Find elements common to both $A$ and $B$: $$ A \cap B = \{6,7,8,10,13,14,15\} $$ **Final answers:** - $A \cup B = \{1,2,4,5,6,7,8,9,10,11,13,14,15,16,18,19\}$ - $A \cap B = \{6,7,8,10,13,14,15\}$