/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 34 Find each of the following sets.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 34

Find each of the following sets. \(C \cup \varnothing\)

Short Answer

Expert verified
\(C \cup \varnothing = C\)

Step by step solution

01

Understanding the sets

We have two sets here: set \(C\) and the empty set. The empty set, denoted by \(\varnothing\), does not contain any elements. Set \(C\) can contain any number of elements, let's generically denote these elements as \(c_1, c_2, \ldots, c_n\).
02

Understanding Union of Sets

The union of two sets, represented by \(C \cup \varnothing\), includes all the elements that are in set \(C\) or in the empty set, or in both. The resulting set will contain each element only once, even if that element is present in both the joined sets.
03

Performing the Union Operation

Considering the empty set has no elements, the union of set \(C\) and the empty set will then be the set \(C\) itself, which contains elements \(c_1, c_2, \ldots, c_n\). Meaning \(C \cup \varnothing = C\) because there are no elements in the empty set to add to set \(C\) during the union operation.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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. \(C^{\prime} \cap\left(A \cup B^{\prime}\right)\)

Describe the Venn diagram for two disjoint sets. How does this diagram illustrate that the sets have no common elements?

In Exercises 1-12, 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. \(\left(A^{\prime} \cap B\right) \cup\left(A^{\prime} \cap C^{\prime}\right)\)

In Exercises 45-48, construct a Venn diagram illustrating the given sets. \(A=\\{4,5,6,8\\}, B=\\{1,2,4,5,6,7\\}\), \(C=\\{3,4,7\\}, U=\\{1,2,3,4,5,6,7,8,9\\}\)

A winter resort took a poll of its 350 visitors to see which winter activities people enjoyed. The results were as follows: 178 people liked to ski, 154 people liked to snowboard, and 49 people liked to ski and snowboard. How many people in the poll liked to ski or snowboard?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.