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Chapter 2: Problem 118
What is a set?
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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. \(\left(C^{\prime} \cap A\right) \cup\left(C^{\prime} \cap B^{\prime}\right)\)
Construct a Venn diagram illustrating the given sets. \(A=\\{+,-, \times, \div, \rightarrow, \leftrightarrow\\}\) \(B=\\{\times, \div, \rightarrow\\}\) \(C=\\{\wedge, \vee, \rightarrow, \leftrightarrow\\}\) \(U=\\{+,-, \times, \div, \wedge, \vee, \rightarrow, \leftrightarrow, \sim\\}\)
A pollster conducting a telephone poll asked three questions: 1\. Are you religious? 2\. Have you spent time with a person during his or her last days of a terminal illness? 3\. Should assisted suicide be an option for terminally ill people? a. Construct a Venn diagram with three circles that can assist the pollster in tabulating the responses to the three questions. b. Write the letter b in every region of the diagram that represents all religious persons polled who are not in favor of assisted suicide for the terminally ill. c. Write the letter \(\mathrm{c}\) in every region of the diagram that represents the people polled who do not consider themselves religious, who have not spent time with a terminally ill person during his or her last days, and who are in favor of assisted suicide for the terminally ill. d. Write the letter \(d\) in every region of the diagram that represents the people polled who consider themselves religious, who have not spent time with a terminally ill person during his or her last days, and who are not in favor of assisted suicide for the terminally ill. e. Write the letter \(e\) in a region of the Venn diagram other than those in parts (b)-(d) and then describe who in the poll is represented by this region.
Let
$$
\begin{aligned}
U &=\\{x \mid x \in \mathbf{N} \text { and } x<9\\} \\
A &=\\{x \mid x \text { is an odd natural number and } x<9\\} \\
B &=\\{x \mid x \text { is an even natural number and } x<9\\} \\
C &=\\{x \mid x \in \mathbf{N} \text { and } 1
A survey of 75 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 29 students got the news from newspapers, 43 from television, and 7 from both newspapers and television. Of those surveyed, a. How many got the news from only newspapers? b. How many got the news from only television? c. How many got the news from newspapers or television? d. How many did not get the news from either newspapers or television?
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