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Set Operations

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

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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