suppose that 100 of the 120 mathematics students at a college taje at least one of the language french,german and russian .also suppose 65 study french , 45 study german 42 study russian,20 study french and german ,25 study french and russian ,15 study german and russian . find the students studying German only
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Answer:
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Step-by-step explanation:
Let F = set of French language students, G = set of German language students, R = set of Russian language students
Given: n(F union G union R) = 100
n(F) + n(G) + n(R) - n(F intersect G) - n(G intersect R) - n(R intersect F) + n(F intersect G intersect R) = 100
65 + 45 + 42 - 20 - 15 - 25 + n(F intersect G intersect R) = 100
92 + n(F intersect G intersect R) = 100
n(F intersect G intersect R) = 8
hence answer is 8.
With this value, the other parts can be solved (try it!). Draw a Venn diagram to help you visualise the problem.
Given : 100 of 120 students at a college take at least one of the languages France, Germany, and Russia
65 study France, 45 study Germany ,42 study Russia,
20 study France and Germany,
25 study France and Russia
15 study Germany and Russia.
To Find : number of students
(a) who study all three language
(b) who study only Russia
(c)who study France or Germany
Solution:
100 of 120 students at a college take at least one of the languages France, Germany, and Russia
F ∪ G ∪ R = 100
F ∪ G ∪ R = F + G + R - F ∩ G - R ∩ G - F ∩ R + F ∩ G ∩ R
=> 100 = 65 + 45 + 42 - 20 - 15 - 25 + F ∩ G ∩ R
=> 100 = 92 + F ∩ G ∩ R
=> F ∩ G ∩ R = 8
8 study all three language
study only Germany =G - R ∩ G - F ∩ G + F ∩ G ∩ R
= 45 - 15 - 20 + 8
= 18
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