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Problem 12

Let $$ \begin{aligned} U &=\\{1,2,3,4,5,6,7\\} \\ A &=\\{1,3,5,7\\} \\ B &=\\{1,2,3\\} \\ C &=\\{2,3,4,5,6\\} \end{aligned} $$ Find each of the following sets. \((B \cup C)^{\prime} \cap A\)

Problem 13

Write a word description of each set. (More than one correct description may be possible.) \(\\{6,7,8,9, \ldots, 20\\}\)

Problem 13

Write \(\subseteq\) or \(\nsubseteq\) in each blank so that the resulting statement is true. \(\varnothing\) ____ \(\\{2,4,6\\}\)

Problem 14

Let $$ \begin{aligned} U &=\\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\\} \\ A &=\\{\mathrm{a}, \mathrm{g}, \mathrm{h}\\} \\ B &=\\{\mathrm{b}, \mathrm{g}, \mathrm{h}\\} \\ C &=\\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\\} \end{aligned} $$ Find each of the following sets. \(A \cap(B \cup C)\)

Problem 14

Write \(\subseteq\) or \(\nsubseteq\) in each blank so that the resulting statement is true. \(\varnothing\) ___ \(\\{1,3,5\\}\)

Problem 14

Write a word description of each set. (More than one correct description may be possible.) \(\\{9,10,11,12, \ldots, 25\\}\)

Problem 15

Let \(U=\\{1,2,3,4, \ldots\\}\) \(A=\\{1,2,3,4, \ldots, 20\\}, B=\\{1,2,3,4, \ldots, 50\\}\) \(C=\\{2,4,6,8, \ldots\\}\), and \(D=\\{1,3,5,7, \ldots\\}\) Use the roster method to write each of the following sets. \(C^{\prime}\)

Problem 15

Let $$ \begin{aligned} U &=\\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}\\} \\ A &=\\{\mathrm{a}, \mathrm{g}, \mathrm{h}\\} \\ B &=\\{\mathrm{b}, \mathrm{g}, \mathrm{h}\\} \\ C &=\\{\mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\\} \end{aligned} $$ Find each of the following sets. \((A \cup B) \cap(A \cup C)\)

Problem 15

In Exercises 15-32, express each set using the roster method. The set of the four seasons in a year

Problem 15

Write \(\subseteq\) or \(\nsubseteq\) in each blank so that the resulting statement is true. \(\\{2,4,6\\}\) ___ \(\varnothing\)

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