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Chapter 2: Problem 15
In Exercises 15-32, express each set using the roster method. The set of the four seasons in a year
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Assume \(A \neq B\). Draw a Venn diagram that correctly illustrates the relationship between the sets. \(A \cap B=B\)
Describe what is meant by the complement of a set.
Use the Venn diagram and the given conditions to determine the number of elements in each region, or explain why the conditions are impossible to meet. \(n(U)=42, n(A)=26, n(B)=22, n(C)=25\) \(n(A \cap B)=17, n(A \cap C)=11, n(B \cap C)=9\) \(n(A \cap B \cap C)=5\)
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. \((A \cup B)^{\prime} \cap C\)
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. \((A \cup B \cup C)^{\prime}\)
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