In a survey among 100 college students, it was found that 56 of them speak at least one language. 35 of them speak English, 15 speak Japanese and 30 speak Mandarin. 9 speak English and Japanese, 7 speak Mandarin and Japanese, and 12 speak English and Q2. Mandarin. Let E = English M= Mandarin J = Japanese x= Number of college students who can speak English, Japanese and Mandarin. а) Display the information above in the Venn diagram shown below in terms of x. U E M J b) Find the number of college students who can speak all the three languages. c) How many of the college students can speak Mandarin and Japanese but not English? d) How many of the college students can speak exactly one language?

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Subject: Discrete Mathematics

In a survey among 100 college students, it was found that 56 of them speak at least one
language. 35 of them speak English, 15 speak Japanese and 30 speak Mandarin. 9 speak
English and Japanese, 7 speak Mandarin and Japanese, and 12 speak English and
Q2.
Mandarin.
Let E = English
M= Mandarin
J = Japanese
x= Number of college students who can speak English, Japanese and Mandarin.
а)
Display the information above in the Venn diagram shown below in terms of x.
U
E
M
J
b)
Find the number of college students who can speak all the three languages.
c)
How many of the college students can speak Mandarin and Japanese but not
English?
d)
How many of the college students can speak exactly one language?
Transcribed Image Text:In a survey among 100 college students, it was found that 56 of them speak at least one language. 35 of them speak English, 15 speak Japanese and 30 speak Mandarin. 9 speak English and Japanese, 7 speak Mandarin and Japanese, and 12 speak English and Q2. Mandarin. Let E = English M= Mandarin J = Japanese x= Number of college students who can speak English, Japanese and Mandarin. а) Display the information above in the Venn diagram shown below in terms of x. U E M J b) Find the number of college students who can speak all the three languages. c) How many of the college students can speak Mandarin and Japanese but not English? d) How many of the college students can speak exactly one language?
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