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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 1875 people chose bratwurst and 2003 people chose sweet corn. Among those who chose bratwurst, 333 did not choose sweet corn.   Construct a Venn diagram to represent your assigned problem. Include capital letter labels for all sets and indicate what each label represents. 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

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 1875 people chose bratwurst and 2003 people chose sweet corn. Among those who chose bratwurst, 333 did not choose sweet corn.   Construct a Venn diagram to represent your assigned problem. Include capital letter labels for all sets and indicate what each label represents. 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

Algebra and Trigonometry (6th Edition)
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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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

1875 people chose bratwurst and 2003 people chose sweet corn. Among those who chose bratwurst, 333 did not choose sweet corn.

 

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


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

 

 

Given: A. 2,545 = Total attendees at picnic 1,875 = Number of attendees who chose bratwurst 2,003 = Number of attendees who chose sweet corn 333 = Number of attendees who chose bratwurst but not sweet corn A = {# of people who chose bratwurst} B = {# of people who chose sweet corn} AnB = {# of people who chose both bratwurst and sweet corn} Now, B. n(A)=1875, n(B)= 2003, n(An B)=1875-333 =1542 n(A-B) = n(A)-n(ANB) = 333 n(B-A) = n(B)-n(ANB) = 461 A 333 A = {333} B = {461} AnB = {1545) 1542 B 461 U 209
Transcribed Image Text:Given: A. 2,545 = Total attendees at picnic 1,875 = Number of attendees who chose bratwurst 2,003 = Number of attendees who chose sweet corn 333 = Number of attendees who chose bratwurst but not sweet corn A = {# of people who chose bratwurst} B = {# of people who chose sweet corn} AnB = {# of people who chose both bratwurst and sweet corn} Now, B. n(A)=1875, n(B)= 2003, n(An B)=1875-333 =1542 n(A-B) = n(A)-n(ANB) = 333 n(B-A) = n(B)-n(ANB) = 461 A 333 A = {333} B = {461} AnB = {1545) 1542 B 461 U 209
i. ii. iii. iv. C. i. ii. iv. Number of attendees who chose bratwurst = 1875 Number of attendees who chose sweet corn = 2003 elements in group 2 but not in group 1 = 461 elements in group 1 or group 2 =n(A U B) = n(A) + n(B)-n(ANB) =1875+2003-1542 =2336 element in neither group-1 or group-2 = n(U) - n(AUB) = 2545-2336 = 209 element in both group 1 and group 2 = (ANB) = 1875-333=1542 elements in group-2 but not group-1 n (B-A) = n (B) - n(A U B) = 2003-1542 = 461 elements in group-1 or group-2 n(A U B) = n(A) + n(B) -n(ANB) = 1875 + 2003 - 1542 = 2336 elements in neither group-1 or group-2 n((ANB)') = n(U) - n(A U B) =2545-2336 =209
Transcribed Image Text:i. ii. iii. iv. C. i. ii. iv. Number of attendees who chose bratwurst = 1875 Number of attendees who chose sweet corn = 2003 elements in group 2 but not in group 1 = 461 elements in group 1 or group 2 =n(A U B) = n(A) + n(B)-n(ANB) =1875+2003-1542 =2336 element in neither group-1 or group-2 = n(U) - n(AUB) = 2545-2336 = 209 element in both group 1 and group 2 = (ANB) = 1875-333=1542 elements in group-2 but not group-1 n (B-A) = n (B) - n(A U B) = 2003-1542 = 461 elements in group-1 or group-2 n(A U B) = n(A) + n(B) -n(ANB) = 1875 + 2003 - 1542 = 2336 elements in neither group-1 or group-2 n((ANB)') = n(U) - n(A U B) =2545-2336 =209
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