Question

In a survey of students, 21 students liked Arts stream, 26 liked Commerce stream and 29
liked Science stream. 14 students liked Arts and Commerce, 10 students liked Arts and
Science, 8 students liked Commerce and Science and 6 liked all three streams. Atleast
how many students like Arts or Commerce or Science stream ? Every one liked atleast one
stream.​

Answer 1

• 38 because others like two subject

Answer 2

Given : in a survey of students, 21 students liked Arts stream, 26 liked Commerce stream and 29  liked Science stream. 14 students liked Arts and Commerce, 10 students liked Arts and  Science, 8 students liked Commerce and Science and 6 liked all three streams.

To Find : Atleast  how many students like Arts or Commerce or Science stream

Solution:

Arts  n(A)  = 21

Commerce n(C) = 26

Science n(S)  = 29

Arts and Commerce  n(A∩C)  = 14

Arts and Science  n(A∩S)  = 10

Commerce and Science n(C∩S)  = 8

all three streams.  n (A∩C∩S)  = 6

none = 0

Atleast  how many students like Arts or Commerce or Science stream

n(A ∪ C ∪ S) = n(A) + n(C) + n(S)  - n(A∩C) - n(A∩S)  - n(C∩S) + n (A∩C∩S)

=>  n(A ∪ C ∪ S) = 21 + 26 + 29  - 14 - 10 - 8 + 6

= 50

 Atleast 50 students like Arts or Commerce or Science stream

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