Assigned Problem: At a large company picnic attended by 2,545 people, two of the food items served are bratwurst and roasted sweet corn.  Let the following subsets be defined:  Group 1: attendees who chose bratwurst Group 2: attendees who chose sweet corn 1,875 people chose bratwurst and 2,003 people chose sweet corn. Among those who chose bratwusrt, 333 did not choose sweet corn.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Assigned Problem:
At a large company picnic attended by 2,545 people, two of the food items served are bratwurst and roasted sweet corn. 

Let the following subsets be defined: 
Group 1: attendees who chose bratwurst
Group 2: attendees who chose sweet corn

1,875 people chose bratwurst and 2,003 people chose sweet corn. Among those who chose bratwusrt, 333 did not choose sweet corn. 


 

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Follow-up Question

I'm struggling with what symbols were used down in the handwritten portion of the follow up answer. 

→n (ANB)
ท
n (A) = 1875,
Now
ü)
(in)
(w)
2
n (A-B).
n (A) n (An (3)
2 (B-A) =
n (B) = n(ADB) =
a) The Venn diagteam is given by
209
333
=
1875-333
=
n (B) = 2003,
5
A
✓
1) Number of altendess who choose bratwurst = 1875
Number of altendess who chose sweet corn = 2003
elements in Group 2 but not group1 = 461
elements in croup-1 or group-2
n (AUB) =
n (A) + n(B) = n(ANB)
1875 + 2003
1542
=1542
B
1542 461
= 333
461
-
= 23 36.
element in neiter group-1 nor
group-2
n(u) n (AUB) = 2545-23 36 = 209
-
Transcribed Image Text:→n (ANB) ท n (A) = 1875, Now ü) (in) (w) 2 n (A-B). n (A) n (An (3) 2 (B-A) = n (B) = n(ADB) = a) The Venn diagteam is given by 209 333 = 1875-333 = n (B) = 2003, 5 A ✓ 1) Number of altendess who choose bratwurst = 1875 Number of altendess who chose sweet corn = 2003 elements in Group 2 but not group1 = 461 elements in croup-1 or group-2 n (AUB) = n (A) + n(B) = n(ANB) 1875 + 2003 1542 =1542 B 1542 461 = 333 461 - = 23 36. element in neiter group-1 nor group-2 n(u) n (AUB) = 2545-23 36 = 209 -
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Follow-up Question

I am not understanding how the cardinality was determined. Could you give an explanation on each set of cardinality? In words, not the work to determine cardinality. 

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Follow-up Question

 Construct a Venn diagram to represent your assigned problem. Include capital letter labels for all sets and indicate what each label represents.
 

B.  Use the set notation symbols (∪,',∩) and set labels from part A to express each of the following sets:

•  elements in both Group 1 and Group 2

•  elements in Group 2 but not Group 1

•  elements in Group 1 or Group 2

•  elements in neither Group 1 nor Group 2
 

C.  Determine the cardinality of each of the following sets, including an explanation of the process for how you determined the cardinality:

•  elements in both Group 1 and Group 2

•  elements in Group 2 but not Group 1

•  elements in Group 1 or Group 2

•  elements in neither Group 1 nor Group 2
 

 

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