a) How many students enjoy both acting and singing? b) How many students enjoy acting or enjoy singing? c) How many students enjoy dancing and singing but not acting? d) How many students enjoy dancing only?

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.1: Counting
Problem 84E
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2. In a freshman class of 60 students, there are 30 who enjoy dancing, 10 who enjoy
acting, 39 who enjoy singing. There are 15 students who enjoy both dancing and
singing, 5 who enjoy both dancing and acting, 20 who enjoy singing only and not
dancing nor acting. Only four students enjoy dancing, singing and acting. Give the
exact values for the following questions and show your solution. Let =set of all
freshmen, D=set of freshmen who enjoy dancing, A=set of freshmen who enjoy
acting, S=set of freshmen who enjoy singing. For each item below, express the set
whose cardinal no. is needed in terms of the sets D, A and S.
a) How many students enjoy both acting and singing?
b) How many students enjoy acting or enjoy singing?
c) How many students enjoy dancing and singing but not acting?
d) How many students enjoy dancing only?
Transcribed Image Text:2. In a freshman class of 60 students, there are 30 who enjoy dancing, 10 who enjoy acting, 39 who enjoy singing. There are 15 students who enjoy both dancing and singing, 5 who enjoy both dancing and acting, 20 who enjoy singing only and not dancing nor acting. Only four students enjoy dancing, singing and acting. Give the exact values for the following questions and show your solution. Let =set of all freshmen, D=set of freshmen who enjoy dancing, A=set of freshmen who enjoy acting, S=set of freshmen who enjoy singing. For each item below, express the set whose cardinal no. is needed in terms of the sets D, A and S. a) How many students enjoy both acting and singing? b) How many students enjoy acting or enjoy singing? c) How many students enjoy dancing and singing but not acting? d) How many students enjoy dancing only?
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