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Use Venn diagrams to answer each of the following
questions. You must show your Venn diagram for each
problem. 1. A survey of 80 sophomores at a certain
western college showed the following:
36 take English ,32 take history
32 take political science
16 take history and English
16 take political science and history ,14 take political
science and English
6 take all three
How many students:
a) take English and neither of the
other two? ____________
b) Take none of the three
courses? ____________
c) take history, but neither of
the other two? ____________
d) take political science and history but not English?
____________
e) do not take political science?
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Answer Posted / smitha
Suppose g be the no. of students taking all three subjects.
therefore, g = 6
Suppose "e + g" students take english and history, "d + g"
students take english and political science, "f + g"
students take political science and history, thus,
e + g = 16
f + g = 16
d + g = 14
Let a, b, c be t he number of students taking only English,
History or Political science respectively.
Thus, we get the following equations:
a + e + g + d = 36
b + e + g + f = 32
c + d + g + f = 32
Solving the above 7 equations we get,
a = 12, b = 6, c = 8
Thus answers are as follows:
a) 12 (bcz a = 12)
b) 80 - (a+b+c+d+e+f+g) = 80 - 60 = 20
c) 6 (bcz b = 6)
d) 10 (bcz f = 10)
e) (a+b+c+d+e+f+g) - (c+d+f+g) = 60 - 32 = 28
| Is This Answer Correct ? | 24 Yes | 1 No |
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