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# Help me please im confused

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A survey conducted among 150 high school students revealed that

63 students like math

85 students like english

62 students like History

31 students like both math and english

25 students like both math and history

20 students like both english and history

8 students like all the three subject

How many highschool students like Math only?English only?History only?

How many highschool students did not like any of the three subjects?

This is related to about the Kind of Sets And Venn Diagram

Intersection of sets, Union of sets, Venn Diagram

Jun 19, 2019
edited by Guest  Jun 19, 2019
edited by Guest  Jun 19, 2019
edited by Guest  Jun 19, 2019

#1
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For what are you looking?

Jun 19, 2019
#2
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Here is the Venn diagram.....as you can add up...there are only 142 students in the diagram....that means 8 do not like any of the subjects

Math only = 15     English only = 42   History only = 25

Jun 19, 2019
#3
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Using the Principle of Inclusion and Exclusion, we have \(63+85+62-31-25-20+8=142\) students. Thus, eight of them like neither of the three subjects.

Math Only: 63-31-25+8=7+8=15 students.

English Only: 85-31-20+8=42 students.

History Only: 62-25-20+8=25 students.

Jun 19, 2019
#4
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Math only = 15

English only = 42

History only = 25

8 did not like any

Jun 19, 2019