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Set Operations

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

Relative Complement

         

If \(A\) and \(B\) are subsets of the set \(U=\{0,3,5,10,12,16,18\}\) such that \[A \cap B^{C}=\{3,5\}, A^{C} \cap B=\{10,12\}, A^{C} \cap B^{C}=\{16,18\},\] then which of the following is equal to \(A \cap B?\)

Details and assumptions

You may choose to read the summary page Set Notation.

Consider the ground set \[U=\{x \mid x \mbox{ is a positive integer } \leq 17\}. \] If \(A=\{1,2,\ldots,5\}\) and \(B\) is a subset of \(U\) such that \[A \cap B=\{4, 5\}, (U \setminus A) \cap (U \setminus B)=\{16, 17\},\] what is \(\lvert B \rvert?\)

Consider the ground set \[U=\{x \mid x \mbox{ is a positive integer } \leq 35\} \] and let \(A\) and \(B\) be two subsets of \(U\) such that \[A=\{1, 2, 3, \ldots, 17\}, \; A \setminus(A \setminus B)=A.\] What is \(\lvert (U \backslash A) \cup B \rvert?\)

Details and assumptions

You may choose to read the summary page Set Notation.

Consider the sets \[A=\{x \mid 3 \leq x < 50\}, B=\{x \mid x \leq 0 \text{ or } x > 43\}.\] How many integers are there in the set \(A \setminus B?\)

Details and assumptions

You may choose to read the summary page Set Notation.

Consider a ground set \(U\) and let \(A\) and \(B\) be two subsets of \(U.\) If \[ \lvert U \rvert=70, \lvert A \rvert=37, \lvert A \cap B \rvert=13, \lvert A \cup B \rvert=48,\] what is \( \lvert U \setminus B^c \rvert?\)

Details and assumptions

You may choose to read the summary page Set Notation.

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