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Familiarize yourself with the foundational notation, tools and concepts for the operations that are applied to sets.

Consider the sets \[\begin{align} A &=\{x \mid -8 < x < 4, x \text{ is an integer} \}\\ B &=\{x \mid -2 < x \leq 11, x \text{ is an integer} \}. \end{align}\] What is \( \lvert A \triangle B \rvert ?\)

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Consider two sets:

\[ A = \{ 5, 6, 7, 8, 9, 10 \} \\ B = \{ 6, 8, 10, 16, 24 \} \]

What is \( \lvert A \triangle B \rvert \)?

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Consider the sets \[A=\{1,2,a+7\}, B=\{a+3, a^2, -a+10, 16\}.\] If \(A \cap B=\{1, 16\},\) what is the sum of all the elements in the set \(A \triangle B?\)

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If sets \(A\) and \(B\) satisfy \[\begin{align} A & =\{23, 11, 55, 6, 4, 18, 37 \},\\ A\cap B & =\{37, 55\}, \\ \lvert A \triangle B \rvert & =5, \end{align}\] what is the sum of all the elements in the set \(B?\)

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If \(A\) and \(B\) are two sets such that \[|A|=24, |B|=17, |B-A|=9,\] what is the value of \( \lvert A \triangle B \rvert ?\)

**Details and assumptions**

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