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 and P . Is any of B , E and P a subset of one of the others (beside itself)? Write a verbal description of P ′ . Find B ′ ∩ P ′ and describe it in words. Find E ′ ∩ P and describe it in words. Dow Jones Industrial Averages Beginning Ending Percent Year Value Value 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 % Source: Dow Jones and Company
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 and P . Is any of B , E and P a subset of one of the others (beside itself)? Write a verbal description of P ′ . Find B ′ ∩ P ′ and describe it in words. Find E ′ ∩ P and describe it in words. Dow Jones Industrial Averages Beginning Ending Percent Year Value Value 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 % Source: Dow Jones and Company
Solution Summary: The author explains how to determine the elements of B,EandP..
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
and
P
.
Is any of
B
,
E
and
P
a subset of one of the others (beside itself)?
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