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.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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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