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Q61.

Expert-verifiedFound in: Page 11

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

Graph the set

$\left(-2,0\right)\cup \left(-1,1\right)$

The Graph of the given set is:

If $a<b$, then the open interval from *a* to *b* consists of all numbers between *a* and *b* and is denoted by $\left(a,b\right)$. The closed interval from *a* to *b* includes the endpoints and is denoted by $\left[a,b\right]$. If points are included in the interval, they are represented by dark circles and if the points are not included in the interval, they are represented by hollow circles on the number line.

Using set-builder form, we can write the intervals as inequality:

$\left(a,b\right)=\left\{x|a<x<b\right\}\phantom{\rule{0ex}{0ex}}\left[a,b\right]=\left\{x|a\le x\le b\right\}$

If *S* and *T* are sets, then their union $S\cup T$ is the set that consists of all elements that are in *S* or *T* (or in both).

$\begin{array}{l}\left(-2,0\right)\cup \left(-1,1\right)\\ =\left\{x|-2<x<0\right\}\cup \left\{x|-1<x<1\right\}\\ =\left\{x\right|-2<x<0\text{or}-1<x<1\}\\ =\left\{x\right|-2<x<1\}\\ =\left(-2,1\right)\end{array}$

We will graph all three intervals:

$\left(-2,0\right)$

It includes all the numbers between -2 and 0.

$\left(-1,1\right)$

It includes all the numbers between -1 and 1

$\left(-2,0\right)\cup \left(-1,1\right)=\left(-2,1\right)$

It includes all the numbers between -2 and 1

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