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Set Operations

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

Sets - Composition of Operations

         

What is

\[ ( A \backslash B ) \cup ( B \backslash A)? \]

If \[A=\{2,5,6,18,20\}, B=\{1,2,6,20,22\},\] then which of the following is equal to \(\left((A \setminus B) \cup (B \setminus A)\right) \cap A?\)

Details and assumptions

You may choose to read the summary page Set Notation.

Consider the ground set \[U=\{x \mid x \mbox{ is a non-negative integer } \leq 9\} \] and let \(A\) and \(B\) be two subsets of \(U.\) If \[A^c \cap B^c=\{8, 9\},\] what is \(\lvert A \cup B \rvert?\)

The sets \[A=\{12,14,16\}, B=\{13,15,17\}\] are subsets of a universal set \(U\). If \(A \cup B=U,\) then what is the sum of the elements of the set \[\left((A \cap B) \cup (A^{C} \cap B)\right) \cup \left((A^{C} \cap B^{C}) \cup (A \cap B^{C})\right)?\]

Details and assumptions

You may choose to read the summary page Set Notation.

Suppose \(A\) and \(B\) are the following subsets of a universal set \(U\): \[A=\{1,3,5,10,13,23\}, B=\{2,4,6,14\}.\] What is the number of elements of the set \[A \setminus \left((A \setminus B) \cup \left(A \setminus B^{C}\right)\right)?\]

Details and assumptions

You may choose to read the summary page Set Notation.

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