Set 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
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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
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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.