Chapter 0.1, Problem 47E

Dow Jones Industrial Average The following table shows information about each year's Dow Jones Industrial average beginning value, ending value, and annual percent change for the years from $2005$ to $2016$. Let $B$ be the set of years when the beginning value was less than $13,000$. Let $E$ be the set of years when the ending value was greater than $12,000$. Let $P$ be the set of years when the annual percent change was less than $7\%$.

List the elements of $B,E\text{and}P$.

Is any of $B,E\text{and}P$ a subset of one of the others (beside itself)?

Write a verbal description of $P^{\prime }$.

Find $B^{\prime }\cap P^{\prime }$ and describe it in words.

Find $E^{\prime }\cap P$ and describe it in words.

$\begin{array}{c}\text{Dow}\text{Jones}\text{Industrial}\text{Averages}\\ \begin{array}{cccc}& \text{Beginning}& \text{Ending}& \text{Percent}\\ \text{Year}& \text{Value}& \text{Value}& \text{Change}\\ 2005& 10,783.01& 10,717.50& -0.61\%\\ 2006& 10,717.50& 12,463.15& 16.29\%\\ 2007& 12,463.15& 13,264.82& 6.43\%\\ 2008& 13,264.82& 8776.39& -33.84\%\\ 2009& 8776.39& 10,428.05& 18.82\%\\ 2010& 10,428.05& 11,577.51& 11.02\%\\ 2011& 11,577.51& 12,217.56& 5.53\%\\ 2012& 12,217.56& 13,104.14& 7.26\%\\ 2013& 13104.14& 16,576.66& 26.50\%\\ 2014& 16,576.66& 17,823.07& 7.52\%\\ 2015& 17,823.07& 17,425.03& -2.23\%\\ 2016& 17,425.03& 19,726.60& 13.42\%\end{array}\end{array}$

Source: Dow Jones and Company