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Chapter 2: Problem 35

Find each of the following sets. \(A \cap \varnothing\)

Short Answer

Expert verified
\(\varnothing\)

Step by step solution

01

Understand the symbols

\(\cap\) means intersection which for two sets is the set of elements common to both. \(\varnothing\) is the notation for an empty set, which means a set with no elements.
02

Determine Intersection with Empty Set

Any set intersected with an empty set yields an empty set. This is because there are no elements in an empty set, so there can't be any elements that are common to it and another set. Therefore \(A \cap \varnothing = \varnothing\).

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Most popular questions from this chapter

A pollster conducting a telephone poll at a college campus asked students two questions: 1\. Do you binge drink three or more times per month? 2\. Regardless of your answer to question 1 , are you frequently behind in your school work? a. Construct a Venn diagram that allows the respondents to the poll to be identified by whether or not they binge drink and whether or not they frequently fall behind in school work. b. Write the letter b in every region of the diagram that represents binge drinkers who are frequently behind in school work. c. Write the letter c in every region of the diagram that represents students polled who do not binge drink but who are frequently behind in school work. d. Write the letter d in every region of the diagram that represents students polled who do not binge drink and who do not frequently fall behind in their school work.

In Exercises 13-24, 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. \((B \cup C)^{\prime} \cap A\)

In Exercises 13-24, 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. \(\left(C^{\prime} \cap A\right) \cup\left(C^{\prime} \cap B^{\prime}\right)\)

Describe what is meant by the intersection of two sets. Give an example.

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