Set Differences
1. **Problem Statement:** Given sets \(A = \{0, 2, 4, 6, 8, 10\}\), \(B = \{0, 1, 2, 3, 4, 5, 6\}\), and \(C = \{4, 5, 6, 7, 8, 9, 10\}\), find:
c) \(A - B\)
d) \(B - A\)
---
2. **Step 1: Understand set difference**
- \(A - B\) means elements in \(A\) that are not in \(B\).
- \(B - A\) means elements in \(B\) that are not in \(A\).
3. **Step 2: Calculate \(A - B\)**
- \(A = \{0, 2, 4, 6, 8, 10\}\)
- \(B = \{0, 1, 2, 3, 4, 5, 6\}\)
- Elements in \(A\) but not in \(B\) are \(8\) and \(10\).
So, \(A - B = \{8, 10\}\).
4. **Step 3: Calculate \(B - A\)**
- Elements in \(B\) but not in \(A\) are \(1, 3, 5\).
So, \(B - A = \{1, 3, 5\}\).
---
**Final answers:**
\[
\begin{aligned}
&\text{c) } A - B = \{8, 10\} \\
&\text{d) } B - A = \{1, 3, 5\}
\end{aligned}
\]