Subjects set theory

Set Differences

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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:** \[ \begin{aligned} &\text{c) } A - B = \{8, 10\} \\ &\text{d) } B - A = \{1, 3, 5\} \end{aligned} \]