1.) ( 5 pts.) Let \( L=\{1,2,3,4,6,8,12,24\} \) be the set of the factors of 24 . Let \( M=\{1,2,5,10,25,50\} \) be the set of the factors of 50 . Describe what the set \( L \cap M \) looks like. Also describe what the set \( L \cup M \) looks like. You may use a diagram to help you with your explanation.

To find the intersection \( L \cap M \) and the union \( L \cup M \), let's examine both sets closely. The set \( L \) of factors of 24 is \( \{1, 2, 3, 4, 6, 8, 12, 24\} \), while the set \( M \) of factors of 50 is \( \{1, 2, 5, 10, 25, 50\} \). **Intersection \( L \cap M \)**: This set includes all elements that are common to both \( L \) and \( M \). Looking at both lists, we find: \[ L \cap M = \{1, 2\} \] **Union \( L \cup M \)**: This set includes all unique elements from both \( L \) and \( M \). By combining all numbers from both sets and removing duplicates, we get: \[ L \cup M = \{1, 2, 3, 4, 5, 6, 8, 10, 12, 24, 25, 50\} \] To visually represent this information, you could draw two overlapping circles (like a Venn diagram). One circle represents \( L \) with all its factors inside, the other circle represents \( M \). The overlapping area would highlight \( \{1, 2\} \), demonstrating the intersection, while the entire area covering both circles combined would show the union \( \{1, 2, 3, 4, 5, 6, 8, 10, 12, 24, 25, 50\} \).