1. **State the problem:** We are given two sets: $$B = \{1, 3, 5, 7, 9, 11, 13, 14\}$$ $$a = \{3, 6, 9, 12, 15\}$$ We need to find some common data or relationships between these sets. 2. **Find the intersection of sets $B$ and $a$:** The intersection contains elements that are in both sets. $$B \cap a = \{x \mid x \in B \text{ and } x \in a\}$$ Check each element of $a$ to see if it is in $B$: - 3 is in $B$ - 6 is not in $B$ - 9 is in $B$ - 12 is not in $B$ - 15 is not in $B$ So, $$B \cap a = \{3, 9\}$$ 3. **Find the union of sets $B$ and $a$:** The union contains all elements from both sets without duplicates. $$B \cup a = \{1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15\}$$ 4. **Find the difference $B - a$:** Elements in $B$ but not in $a$. $$B - a = \{1, 5, 7, 11, 13, 14\}$$ 5. **Find the difference $a - B$:** Elements in $a$ but not in $B$. $$a - B = \{6, 12, 15\}$$ **Summary:** - Intersection: $\{3, 9\}$ - Union: $\{1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15\}$ - Difference $B - a$: $\{1, 5, 7, 11, 13, 14\}$ - Difference $a - B$: $\{6, 12, 15\}$ These are the main set operations to analyze the data given.