Explanation Given Information: The survey of 4000 students in a school was taken, 2000 take French (F), 3000 take Spanish (S), 500 take Latin (L), 1500 take both French and Spanish, 300 take both French and Latin, 200 take Spanish and Latin, 50 take all three languages. Calculation: Consider the details given about the survey, Let U represent the number of students surveyed, F represent the students who take French, S represent the students who take Spanish, and L represent the student who take Latin. Then, n ( U ) = 4000 , n ( F ) = 2000 , n ( S ) = 3000 , n ( L ) = 500 , n ( F ∩ S ) = 1500 , n ( L ∩ F ) = 300 , n ( L ∩ S ) = 200 , n ( F ∩ L ∩ S ) = 50 Use the data provided, to complete the Venn diagram given as: Since, there are 50 students, who take all three languages, Now, fill in the rest of Venn diagram by working with remaining information one piece at a time in the reverse order. Since, 1500 students take both French and Spanish, 1500 − 50 = 1450 gives priority to French and Spanish but not Latin. The appropriate region is shown below: Similarly, 200 students give the priorities to Spanish and Latin, 200 − 50 = 150 gives their priorities to Spanish and Latin and not French, The appropriate region is shown below: Similarly, 300 students give the priorities to French and Latin, 300 − 50 = 250 gives their priorities to French and Latin and not Spanish, The appropriate region is shown below: Since n ( F ) = 2000 , so the number of students who take French only is; 2000 − 1450 − 50 − 250 = 2000 − 1500 − 250 = 250 Thus, the number of students who take only French is 250

MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134765723

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 5.3, Problem 49E

To determine

To calculate: The number of people in the set L∪S∪F′.

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Chapter 5.3, Problem 48E

Chapter 5.3, Problem 50E

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Chapter 5 Solutions

MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications (12th Edition)

Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E

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The number of people in the set L ∪ S ∪ F ′ .

Solution Summary: The author explains how to calculate the number of people in the set Lcup Fprime.

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To calculate: The number of people in the set L∪S∪F′.

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Chapter 5 Solutions