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Set Operations

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

Symmetric Difference

         

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

Details and assumptions

You may choose to read the summary page Set Notation.

Consider two sets:

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

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

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 \(A \triangle B?\)

Details and assumptions

You may choose to read the summary page Set Notation.

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 \(B?\)

Details and assumptions

You may choose to read the summary page Set Notation.

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

You may choose to read the summary page Set Notation.

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