In a survey of 260 college students the following data were obtained

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University-Visvesvaraya-College-of-Engineering-Bangalore--->View question

In a survey of 260 college students, the following data were obtained:

->   In a survey of 260 college students, the following data were obtained: 64

had taken a mathematics course, 94 had taken a computer science course,

58 had taken a business course, 28 had taken both a mathematics and a business course, 26 had taken both a mathematics and a computer science course, 22 had taken both a computer science and a business course, and 14 had taken all three types

i.            How many of these students had taken none of the three courses?

ii.   How many had taken only a computer science courses ? -

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Solution:

Given: U=260 |A|=64 |B|=94 |C|=58 |A ∩ C| = 28 |A ∩ B| = 26 |B ∩ C| = 22 |A ∩ B ∩ C| = 14

|A U B U C| =? |B1| =?

|A U B U C| = A + B + C – |A ∩ B| – |B ∩ C| – |A ∩ C| + |A ∩ B ∩ C|

=   64 + 94 + 58 – 26 – 22 – 28 + 14

=   154

i.   |A U B U C| = U – |A U B U C|

=   260 – 154

=   106

ii.|B1| = |B| - |B ∩ C| - |B ∩ A| + |A ∩ B ∩ C|

= 94 – 22 – 26 + 14 = 60

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