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Chapter 2: Problem 120
What is the empty set?
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Describe what is meant by the union of two sets. Give an example.
Use the formula for the cardinal number of the union of two sets to solve Exercises 93-96. Set \(A\) contains 8 letters and 9 numbers. Set \(B\) contains 7 letters and 10 numbers. Four letters and 3 numbers are common to both sets \(A\) and \(B\). Find the number of elements in set \(A\) or set \(B\).
Construct a Venn diagram illustrating the given sets. \(\begin{aligned} A &=\left\\{x_{3}, x_{9}\right\\} \\ B &=\left\\{x_{1}, x_{2}, x_{3}, x_{5}, x_{6}\right\\} \\ C &=\left\\{x_{3}, x_{4}, x_{5}, x_{6}, x_{9}\right\\} \\ U &=\left\\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, x_{9}\right\\} \end{aligned}\)
In Exercises 41-66, 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. \(C \cup \varnothing\)
A pet store surveyed 200 pet owners and obtained the following results: 96 people owned cats, 97 people owned dogs, and 29 people owned cats and dogs. How many people in the survey owned cats or dogs?
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