Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
In a survey of 1000 students, .623 like chocolate ice cream 513 like vanilla ice cream • 378 like strawberry ice cream . 301 like both chocolate and vanilla . • 245 like both chocolate and strawberry . 196 like both vanilla and strawberry 120 like none of these flavors How many students like all three flavors? Enter the exact integer. Hint 1: The principle of inclusion-exclusion for three sets is: |CUVUS| = |C| + |V| + |S| - |Cnv|-|CnS - VnS+Cnvs Now, convince yourself with a Venn diagram that by adding (CUVUS) (the number of students who liked none of these flavors) to both sides of this equation, that the LHS will equal 1000 (each student either liked at least one of the three flavors or did not). The only missing value then becomes |CVS), the number of students who liked all three flavors. If you do draw a Venn diagram, filling in the regions with the appropriate numbers, it is good to check that your work matches the given information. Hint 2: Alternatively, find CUVUS using the number of students who liked none of the flavors and the fact that there are 1000 students in the universal set. This is similar to how we did the example in the slides.
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Transcribed Image Text:In a survey of 1000 students, .623 like chocolate ice cream 513 like vanilla ice cream • 378 like strawberry ice cream . 301 like both chocolate and vanilla . • 245 like both chocolate and strawberry . 196 like both vanilla and strawberry 120 like none of these flavors How many students like all three flavors? Enter the exact integer. Hint 1: The principle of inclusion-exclusion for three sets is: |CUVUS| = |C| + |V| + |S| - |Cnv|-|CnS - VnS+Cnvs Now, convince yourself with a Venn diagram that by adding (CUVUS) (the number of students who liked none of these flavors) to both sides of this equation, that the LHS will equal 1000 (each student either liked at least one of the three flavors or did not). The only missing value then becomes |CVS), the number of students who liked all three flavors. If you do draw a Venn diagram, filling in the regions with the appropriate numbers, it is good to check that your work matches the given information. Hint 2: Alternatively, find CUVUS using the number of students who liked none of the flavors and the fact that there are 1000 students in the universal set. This is similar to how we did the example in the slides.
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